WASHINGTON — President Biden will travel to Buffalo on Tuesday to denounce the racist massacre in a predominately Black neighborhood as “terrorism motivated by a hateful and perverse ideology,” according to a White House official, who said Mr. Biden would also call for stricter gun control measures.

The president will be confronting the violent white extremism displayed when neo-Nazis and right-wing militias marched into Charlottesville, Va., a moment Mr. Biden has often said drove him to run for president to undertake a “battle for the soul of America.”

But the challenge for a president who came to office preaching unity may be how to take on those preaching hate. While aides made clear that Mr. Biden would denounce the white supremacy and hate speech that appeared to animate the man who opened fire on mostly Black grocery store shoppers last weekend, killing 10 people, it remained unclear how directly the president would link such violence to the political statements of his opponents.

Republican leaders like Representative Elise Stefanik of New York and Fox News hosts like Tucker Carlson have employed the kind of provocative language that encourages racial resentment and served to inject fringe ideas like replacement theory — the idea that Western elites, sometimes manipulated by Jews, want to replace and disempower white Americans — into the mainstream on the political right.

Mr. Biden, while denouncing domestic extremism, has mostly shied away from a sustained effort to tie it to leading conservatives despite pressure from some on the progressive left to offer a more full-throated condemnation.

Whenever Mr. Biden does speak out more assertively about divisive politics, such as on the anniversary of the Jan. 6 attack on the Capitol, he finds himself accused of violating his own promise to bring harmony to the country, leaving him in something of a political box, trapped by his desire to be a unifier while feeling compelled to take on the forces rending the country apart.

“If he strays anywhere beyond thoughts and prayers, predictably people will scream that he’s politicizing this,” said Michael Waldman, who was a speechwriter for President Bill Clinton. “But it was a political crime, ugly political violence. It would be wrong to act otherwise.”

Karine Jean-Pierre, the White House press secretary, said Mr. Biden would call out domestic terrorism during his visit to Buffalo, even if the trip will be focused on comforting “the families of the 10 people whose lives were so senselessly taken in this horrific shooting.”

But Ms. Jean-Pierre stopped short of identifying by name Mr. Carlson or other members of Congress who have espoused the fringe views.

“Watching what happened in Charlottesville was a major factor in the president deciding to run,” Ms. Jean-Pierre said on Monday. “Many of those dark voices still exist today, and the president is determined as he was back then and he is determined today to make sure that we fight back against those forces of hate and evil and violence.”

Mr. Biden and the first lady, Jill Biden, will also visit the Tops market memorial to pay respects to victims of the mass shooting, the official said. They will then meet with law enforcement officials and relatives of the victims before the president delivers a speech that will call out the “racist violence” on Saturday.

The bloodshed is certain to renew the national debate over gun control, which is a prime example of Washington’s paralyzed politics.

As a senator, Mr. Biden helped pass a 10-year assault weapons ban in the 1990s and as vice president he was tasked with developing a reform package after the massacre of 26 children and adults at Sandy Hook Elementary School in Newtown, Conn., in 2012.

The Obama administration issued nearly two dozen modest executive actions but failed to pass legislation. The Biden administration has also struggled to pass gun control legislation. Last year, Mr. Biden called gun violence in the United States “an international embarrassment” and took some steps to address the problem, starting with a crackdown on the proliferation of so-called ghost guns, or firearms assembled from kits.

But the gun lobby’s hold on the Republican Party is unshaken and action on key gun issues, such as universal background checks and a ban on assault weapons, remains stalled in part because of the narrow partisan divide in the Senate.

A White House spokesman said on Monday that the issue remained a top priority for Mr. Biden.

Mr. Biden has taken steps to focus government resources on preventing domestic extremist attacks after the country spent decades prioritizing the threat of foreign terrorism. In a conversation in 2019 with Janet Napolitano, a former homeland security secretary, Mr. Biden recalled the Obama administration’s decision in 2009 to rescind a report warning that U.S. military veterans were vulnerable to recruitment by extremist groups. Mr. Biden said he thought Ms. Napolitano was “prescient in talking about right-wing extremism and violence in America and motivated by white supremacists.”

But the United States has at times struggled to directly acknowledge, let alone develop an effective response to, the threat of domestic extremism. The Trump administration slashed funding for grants issued to nonprofits and law enforcement agencies that focus on domestic terrorism, cutting a budget in the Homeland Security Department from $20 million during the Obama administration to less than $3 million before much of the funding was restored in 2020. Some White House officials also sought to suppress the phrase “domestic terrorism” as President Donald J. Trump’s Justice Department shifted federal prosecutors and F.B.I. agents from investigations into violent white supremacists to cases involving rioters or anarchists.

“You have to know who your enemy is and the threat is,” said Elizabeth Neumann, the assistant homeland security secretary for counterterrorism and threat prevention under Mr. Trump. “Trump was never willing to acknowledge that. Biden has.”

But she said even with the president’s willingness to describe the threat of deadly white supremacy, the federal government has not made enough progress in working with the authorities to prevent violent extremism.

The Biden administration last June unveiled a national strategy to combat violent extremism, calling for additional hiring of intelligence analysts, improving collaboration with social media companies to take down violent videos and increased funding for digital literacy programs to train the public to identify hateful content and resist recruitment by extremists. The F.B.I. issued three times as many domestic terrorism assessments for local authorities in 2021 as it did the previous year, according to a senior official. But the official also acknowledged the difficulty of policing extremist language on online platforms or amplified by commentators while the government is abiding by the First Amendment.

Ms. Napolitano, who serves on Mr. Biden’s intelligence advisory board, said it was clear the United States had not made enough progress in preventing extremist attacks since the deadly Charlottesville riots.

“Treat it almost like a disease instead of crime so we can better diagnose ahead of time,” Ms. Napolitano said. “I think the bully pulpit is the president’s strongest role.”

Senator Chuck Schumer, Democrat of New York and the majority leader, directly called out hard-right Republicans and Mr. Carlson for amplifying themes that are at the heart of the white supremacist replacement theory.

“The subtext is clear,” Mr. Schumer said. “These hard-right MAGA Republicans argue that people of color and minority communities are somehow posing a threat — a threat — to the American way of life. This is replacement theory in a nutshell.”

He is expected to travel to Buffalo on Tuesday with the president and the first lady to meet with the families of the victims, law enforcement and local officials.

Marc Morial, the president of the National Urban League, a civil rights organization, said truly uniting the country required directly calling out those amplifying theories influencing domestic extremism.

“Some people say when you do this you’re promoting division,” Mr. Morial said. But such claims amount to a “diversion,” he added.

“You unite people around purpose,” he said. “You don’t unite people for the sake of being united.