The judge overseeing former President Donald J. Trump’s trial on charges of seeking to overturn the 2020 election denied on Wednesday his attempt to disqualify her from the case for supposedly being biased against him.

In a strongly worded order, the judge, Tanya S. Chutkan of Federal District Court in Washington, rejected claims by Mr. Trump’s lawyers that she had shown bias against the former president in statements she made from the bench in two cases related to the attack on the Capitol by a pro-Trump mob on Jan. 6, 2021.

In the order, Judge Chutkan not only chided Mr. Trump’s lawyers for putting words in her mouth, but she also asserted that the remarks did not betray any animus or unfairness toward Mr. Trump that would warrant the extraordinary step of removing her from the election interference case.

“The statements certainly do not manifest a deep-seated prejudice that would make fair judgment impossible,” she wrote.

Seeking to disqualify a judge is a challenging and precarious move — one that, if it fails (which it often does), runs the risk of annoying the person granted the power to make critical decisions in the case. Mr. Trump’s lawyers filed their recusal motion two weeks ago, after Judge Chutkan handed them a significant defeat by scheduling the trial for March, much earlier than they had requested, but before they had filed any substantive motions to attack the charges Mr. Trump is facing.

A judge’s decision to remain on a case is generally not subject to an immediate appeal — though Mr. Trump’s lawyers could in theory try. Judge Chutkan’s ruling not to disqualify herself came as she considers a potentially significant development in the case: whether to grant the government’s request to impose a gag order on Mr. Trump’s public statements about the case.

In asking Judge Chutkan to step aside, Mr. Trump’s lawyers cited statements she had made about the former president at hearings for two defendants facing sentencing for crimes they committed on Jan. 6.

At one of the hearings, in October 2022, Judge Chutkan told the defendant, Christine Priola, a former occupational therapist in the Cleveland school system, that the people who “mobbed” the Capitol that day showed “blind loyalty to one person who, by the way, remains free to this day.”

At the other hearing, in December 2021, Judge Chutkan told Robert Palmer, a Florida man who had hurled a fire extinguisher at police officers, that the “people who exhorted you and encouraged you and rallied you to go and take action and to fight have not been charged.”

John F. Lauro, a lawyer for Mr. Trump, argued that the remarks, which were made well before Mr. Trump was charged with three overlapping conspiracies to remain in power, undermined confidence that Judge Chutkan could “administer justice neutrally and dispassionately” and were “inherently disqualifying.”

“Although Judge Chutkan may genuinely intend to give President Trump a fair trial and may believe that she can do so,” Mr. Lauro wrote, “her public statements unavoidably taint these proceedings, regardless of outcome.”

Chiding Mr. Trump’s lawyers, Judge Chutkan pointed out that she had never said Mr. Trump “should be prosecuted and imprisoned” as they claimed.

“The defense does not cite any instance of the court ever uttering those words or anything similar,” she wrote.

Indeed, she argued, the lawyers had wrongly interpreted what she had said in Ms. Priola’s case, apparently believing Judge Chutkan had called for Mr. Trump to be jailed when in fact she had merely pointed out that he remained free at that point — which, she noted, was “an undisputed fact.”

Similarly, in Mr. Palmer’s case, Judge Chutkan said, she had made remarks about who had and had not been charged, but “expressly declined to state who, if anyone” should face charges.

Judge Chutkan was careful to acknowledge that recusal could be warranted if a jurist were biased — or even appeared to be biased. But she also noted that an attempt to disqualify a judge from a case could be “wrongfully deployed as a form of ‘judge shopping’” or used as “a procedural weapon to harass opponents and delay proceedings.”