WASHINGTON — Immediately after Merrick B. Garland was sworn in as attorney general in March of last year, he summoned top Justice Department officials and the F.B.I. director to his office. He wanted a detailed briefing on the case that will, in all likelihood, come to define his legacy: the Jan. 6 assault on the Capitol.

Even though hundreds of people had already been charged, Mr. Garland asked to go over the indictments in detail, according to two people familiar with the meeting. What were the charges? What evidence did they have? How had they built such a sprawling investigation, involving all 50 states, so fast? What was the plan now?

The attorney general’s deliberative approach has come to frustrate Democratic allies of the White House and, at times, President Biden himself. As recently as late last year, Mr. Biden confided to his inner circle that he believed former President Donald J. Trump was a threat to democracy and should be prosecuted, according to two people familiar with his comments. And while the president has never communicated his frustrations directly to Mr. Garland, he has said privately that he wanted Mr. Garland to act less like a ponderous judge and more like a prosecutor who is willing to take decisive action over the events of Jan. 6.

Speaking to reporters on Friday, Mr. Garland said that he and the career prosecutors working on the case felt only the pressure “to do the right thing,” which meant that they “follow the facts and the law wherever they may lead.”

Still, Democrats’ increasingly urgent calls for the Justice Department to take more aggressive action highlight the tension between the frenetic demands of politics and the methodical pace of one of the biggest prosecutions in the department’s history.

“The Department of Justice must move swiftly,” Representative Elaine Luria, Democrat of Virginia and a member of the House committee investigating the riot, said this past week. She and others on the panel want the department to charge Trump allies with contempt for refusing to comply with the committee’s subpoenas.

“Attorney General Garland,” Ms. Luria said during a committee hearing, “do your job so that we can do ours.”

This article is based on interviews with more than a dozen people, including officials in the Biden administration and people with knowledge of the president’s thinking, all of whom asked for anonymity to discuss private conversations.

In a statement, Andrew Bates, a White House spokesman, said the president believed that Mr. Garland had “decisively restored” the independence of the Justice Department.

“President Biden is immensely proud of the attorney general’s service in this administration and has no role in investigative priorities or decisions,” Mr. Bates said.

A Justice Department spokesman declined to comment.

The Jan. 6 investigation is a test not just for Mr. Garland, but for Mr. Biden as well. Both men came into office promising to restore the independence and reputation of a Justice Department that Mr. Trump had tried to weaponize for political gain.

For Mr. Biden, keeping that promise means inviting the ire of supporters who say they will hold the president to the remarks he made on the anniversary of the assault on the Capitol, when he vowed to make sure “the past isn’t buried” and said that the people who planned the siege “held a dagger at the throat of America.”

Complicating matters for Mr. Biden is the fact that his two children are entangled in federal investigations, making it all the more important that he stay out of the Justice Department’s affairs or risk being seen as interfering for his own family’s gain.

The department is investigating whether Ashley Biden was the victim of pro-Trump political operatives who obtained her diary at a critical moment in the 2020 presidential campaign, and Hunter Biden is under federal investigation for tax avoidance and his international business dealings. Hunter Biden has not been charged with a crime and has said he handled his affairs appropriately.

Justice Department officials do not keep Mr. Biden abreast of any investigation, including those involving his children, several people familiar with the situation said. The cases involving Hunter Biden and Ashley Biden are worked on by career officials, and people close to the president, including Dana Remus, the White House counsel, have no visibility into them, those people said.

Still, the situation crystallizes the delicate ground that Mr. Biden and Mr. Garland are navigating.

When it comes to Jan. 6, Justice Department officials emphasize that their investigation has produced substantial results already, including more than 775 arrests and a charge of seditious conspiracy against the leader of a far-right militia. More than 280 people have been charged with obstructing Congress’s duty to certify the election results.

And federal prosecutors have widened the investigation to include a broad range of figures associated with Mr. Trump’s attempts to cling to power. According to people familiar with the inquiry, it now encompasses planning for pro-Trump rallies ahead of the riot and the push by some Trump allies to promote slates of fake electors.

The Justice Department has given no public indication about its timeline or whether prosecutors might be considering a case against Mr. Trump.

The House committee investigating the Jan. 6 attack can send criminal referrals to the Justice Department, but only the department can bring charges. The panel is working with a sense of urgency to build its case ahead of this year’s midterm elections, when Republicans could retake the House and dissolve the committee.

Mr. Biden, a longtime creature of the Senate, is aghast that people close to Mr. Trump have defied congressional subpoenas and has told people close to him that he does not understand how they think they can do so, according to two people familiar with his thinking.

Mr. Garland has not changed his approach to criminal prosecutions in order to placate his critics, according to several Justice Department officials who have discussed the matter with him. He is briefed every afternoon on the Jan. 6 investigation, but he has remained reticent in public.

“The best way to undermine an investigation is to say things out of court,” Mr. Garland said on Friday.

Even in private, he relies on a stock phrase: “Rule of law,” he says, “means there not be one rule for friends and another for foes.”

He did seem to acknowledge Democrats’ frustrations in a speech in January, when he reiterated that the department “remains committed to holding all Jan. 6 perpetrators, at any level, accountable under law.”

Quiet and reserved, Mr. Garland is well known for the job he was denied: a seat on the Supreme Court. President Barack Obama nominated him in March 2016 after the death of Justice Antonin Scalia, but Senate Republicans blockaded the nomination.

Mr. Garland’s peers regard him as a formidable legal mind and a political centrist. After graduating from Harvard Law School, he clerked for a federal appeals court judge and Justice William J. Brennan Jr. of the Supreme Court before becoming a top official in the Justice Department under Attorney General Janet Reno. There, he prosecuted domestic terrorism cases and supervised the federal investigation into the Oklahoma City bombing.

His critics say that his subsequent years as an appeals court judge made him slow and overly deliberative. But his defenders say that he has always carefully considered legal issues, particularly if the stakes were very high — a trait that most likely helped the Justice Department secure a conviction against Timothy J. McVeigh two years after the Oklahoma City attack.

During the presidential transition after the 2020 election, Mr. Biden took his time mulling over candidates to be attorney general, according to a senior member of the transition team. He had promised the American people that he would reestablish the department as an independent arbiter within the government, not the president’s partisan brawler.

In meetings, the incoming president and his aides discussed potential models at length: Did Mr. Biden want a strong personality in the job, like Eric H. Holder Jr., who held the post under Mr. Obama? The relatively quick consensus was no.

Did he want someone who would be seen as a political ally? Some in his circle suggested that might be a good model to follow, which is why former Senator Doug Jones of Alabama, a longtime friend of Mr. Biden’s, was once on his shortlist.

But in the end, Mr. Biden went with Mr. Garland, who had a reputation for being evenhanded and independent.

Despite Mr. Biden’s private frustrations with the attorney general, several people who speak regularly to the president said he had praised Mr. Garland as among the most thoughtful, moral and intelligent people he had dealt with in his career.

The two men did not know each other well when Mr. Biden selected him for the job. Mr. Garland had a closer relationship with Ron Klain, Mr. Biden’s chief of staff, than he did with the incoming president.

Officials inside the White House and the Justice Department acknowledge that the two men have less contact than some previous presidents and attorneys general, particularly Mr. Trump and his last attorney general, William P. Barr.

Some officials see their limited interactions as an overcorrection on the part of Mr. Garland and argue that he does not need to color so scrupulously within the lines. But it may be the only logical position for Mr. Garland to take, particularly given that both of Mr. Biden’s children are involved in active investigations by the Justice Department.

The distance between the two men is a sharp departure from the previous administration, when Mr. Trump would often call Mr. Barr to complain about decisions related to his political allies and enemies. Such calls were a clear violation of the longtime norms governing contact between the White House and the Justice Department.

Mr. Biden, a former chairman of the Senate Judiciary Committee, came to his job as president with a classical, post-Watergate view of the department — that it was not there to be a political appendage.

Still, there is unrelenting pressure from Democrats to hold Mr. Trump and his allies accountable for the violence that unfolded at the Capitol on Jan. 6. While there is no indication that federal prosecutors are close to charging the former president, Mr. Biden and those closest to him understand the legal calculations. What Mr. Garland is confronting is anything but a normal problem, with enormous political stakes ahead of the next presidential election.

Federal prosecutors would have no room for error in building a criminal case against Mr. Trump, experts say, given the high burden of proof they must meet and the likelihood of any decision being appealed.

A criminal investigation in Manhattan that examined Mr. Trump’s business dealings imploded this year, underscoring the risks and challenges that come with trying to indict the former president. The new district attorney there, Alvin Bragg, would not let his prosecutors present a grand jury with evidence that they felt proved Mr. Trump knowingly falsified the value of his assets for undue financial gain.

One of the outside lawyers who oversaw the case and resigned in protest wrote in a letter to Mr. Bragg that his decision was “a grave failure of justice,” even if he feared that the district attorney’s office could lose.

At times, Mr. Biden cannot help but get drawn into the discourse over the Justice Department, despite his stated commitment to stay away.

In October, he told reporters that he thought those who defied subpoenas from the House committee investigating the Jan. 6 attack should be prosecuted.

“I hope that the committee goes after them and holds them accountable criminally,” Mr. Biden said. When asked whether the Justice Department should prosecute them, he replied, “I do, yes.”

The president’s words prompted a swift statement from the agency: “The Department of Justice will make its own independent decisions in all prosecutions based solely on the facts and the law. Period. Full stop.”