WASHINGTON — Judge Ketanji Brown Jackson on Tuesday pushed back on Republican attacks on her record, defending her work representing terror detainees and sentencing child sex abusers as she presented herself as a firm believer in judicial restraint fit to be confirmed to a seat on the Supreme Court.

Under intense questioning from senators in a daylong hearing on her nomination, Judge Jackson said repeatedly that she understood the narrow role that judges played in American government and refused to be drawn into political fights such as whether seats should be added to the Supreme Court.

“I am acutely aware that as a judge in our system, I have limited power, and I am trying in every case to stay in my lane,” she said, a formulation she repeated several times during hours of interrogation in what Senator Richard J. Durbin, Democrat of Illinois and the chairman of the Judiciary Committee, called a “trial by ordeal.”

“I don’t think anyone can look at my record and say it is pointing in one direction or another, that it is supporting one viewpoint or another,” she told senators.

While Republicans had initially been wary of the optics of attacking the first Black woman to be put forward for the Supreme Court, some G.O.P. members on the panel — particularly those with presidential ambitions — assailed Judge Jackson’s record in a series of tense exchanges in which they implied that she was soft on crime, particularly when it came to child sexual abuse, and an extremist on matters of race.

Seeing an opening to score political points if not block her confirmation, they hit on midterm campaign themes that have become rallying cries for conservatives and their hard-right base, returning often to the subject of pedophilia, the central false allegation against Democrats that underlies the pro-Trump conspiracy theory QAnon.

Pointing to her writings about and sentencing of child sex offenders, Senator Ted Cruz, Republican of Texas and a classmate of Judge Jackson at Harvard Law School, said he saw “a record of activism and advocacy that concerns sexual predators, that stems back decades and is concerning.”

Democrats, independent analysts and some conservatives have found the Republican attacks on her record on child sex offenders to be distorted and misleading.

Mr. Durbin sought to get ahead of the issue on Tuesday, opening the hearing by asking Judge Jackson what went through her mind on Monday as she sat and listened, with her family looking on, while a host of Republicans accused her of having coddled sex offenders in her rulings and sentencing recommendations. She used the moment to deliver an emphatic response that telegraphed some of her anger at those attacks.

“As a mother and a judge who has had to deal with these cases, I was thinking that nothing could be further from the truth,” Judge Jackson responded. “These are some of the most difficult cases that a judge has to deal with, because we’re talking about sex abuse of children.”

And she gave a lengthy explanation of how she arrived at sentences in such cases.

“I impose a strict sentence and all of the additional restraints that are available in the law,” Judge Jackson said. “I am imposing all of those constraints because I understand how significant, how damaging, how horrible this crime is.”

But the issue surfaced again later Tuesday, when Senator Josh Hawley, Republican of Missouri, grilled her about her decision to sentence an 18-year-old defendant to three months of jail time for possession for images of child sexual abuse. Mr. Hawley, who has led the charge to attack Judge Jackson’s record on sentencing such offenders, repeatedly asked her why she gave the man a shorter sentence than the guidelines recommended.

Judge Jackson, appearing exasperated, argued that Congress had required judges to take into account various factors, including the age of the defendant, and work with the probation office when sentencing defendants. And she insisted that a lighter penalty did not signal tolerance for child sex abuse.

“As a judge who is a mom and has been tasked with the responsibility of actually reviewing the evidence, the evidence that you would not describe in polite company, the evidence that you are pointing to, discussing, addressing in this context, is evidence that I have seen in my role as a judge,” she said. “It is heinous. It is heinous. It is egregious.”

It was a historic and contentious day for Judge Jackson, who was uniformly praised by Democrats for her life story, educational qualifications, judicial record and even her ability to keep a calm demeanor while under assault by Republicans.

“This is a tough place and you are handling it very well,” said Senator Dianne Feinstein, Democrat of California and a veteran of multiple court showdowns.

Democrats sought to frame her experience as a federal public defender as an asset for a judge, giving her an understanding of both sides of the system, even as Republicans worked to portray it as suspect.

“Those of us who spend time in courtrooms know you have to have both skilled prosecutors and defenders,” said Senator Patrick J. Leahy, Democrat of Vermont.

Her supporters also emphasized the strong support Judge Jackson has received from law enforcement groups, and noted that her family members served as police officers, a fact that Judge Jackson said was a source of pride.

“As someone who has had family members on patrol and in the line of fire, I care deeply about public safety,” she said. “I know what it is like to have loved ones who go off to protect and serve and the fear of not knowing whether or not they are going to come home again because of crime in the community.”

At the same time, she said she also recognized that criminal defense attorneys served an important function by assuring that constitutional rights were protected.

“Our system is exemplary throughout the world precisely because we ensure that people who are accused of crimes are treated fairly,” she said. “It is very important to me in that capacity, as a lawyer and citizen.”

But her work on behalf of terror detainees held at Guantánamo Bay, Cuba, drew fire from Republicans who suggested that she had gone too far in her push to free some of them. They cited legal briefs she co-signed that they said called President George W. Bush and Defense Secretary Donald Rumsfeld “war criminals” because some detainees were subjected to torture following the Sept. 11, 2001, attacks.

“Why would you do something like that?” asked Senator John Cornyn, Republican of Texas. “It seems so out of character.”

Judge Jackson said she did not remember that reference and had no intention of disparaging the defense secretary or the president. Later in the hearing, Mr. Durbin explained that the legal brief at issue followed what was essentially a template that volunteer lawyers across the country were using at the time to make arguments and claims for relief against the Bush administration, which said their actions constituted “war crimes.”

“To be clear, there was no time where you called President Bush or Secretary Rumsfeld a ‘war criminal’?”

“No, senator,” Judge Jackson replied.

In a more heated exchange, Senator Lindsey Graham, Republican of South Carolina, also faulted her for trying to win freedom for someone who could return to threaten U.S. security.

“As long as they are dangerous, I hope they’ll die in jail there,” he said. “It doesn’t bother me one bit if they die in prison.”

All four of the detainees Judge Jackson represented for a time were eventually repatriated — three to Afghanistan and one to Saudi Arabia. None were ever tried or convicted of any crime.

One of the sharpest exchanges of the day was with Mr. Cruz, who pressed Judge Jackson not only on her sentencing of child sex offenders but whether she embraced critical race theory, a field of legal study that examines how racism can be embedded in laws and institutions, which has been appropriated by the right as a way to disparagingly describe any discussion of structural racism.

Mr. Cruz asked her whether she had reviewed books taught at Georgetown Day School, a private school in Washington on whose board she serves, where he said young children were being taught about the theory.

It was the first time after hours of questioning that Judge Jackson showed irritation; she paused, sighing heavily, before replying to Mr. Cruz.

“I have not reviewed any of those books, any of those ideas,” Judge Jackson responded. “They do not come up in my work as a judge, which I am, respectfully, here to address.”

She said she did not believe “that any child should be made to feel as though they are racist, or though they are not valued, or they are less than, that they are victims, they are oppressors. I do not believe in any of that.”

Earlier in the day, Mr. Graham also sought to tie Judge Jackson to progressive activists who support her nomination and also back expanding the size of the court among other changes.

“Did you notice that people from the left were cheering you on?” he asked.

“A lot of people were cheering me on,” Judge Jackson replied.