The judge who oversaw Donald J. Trump’s Manhattan criminal trial declined for a third time to step aside from the case, rebuking the former president’s lawyers for claiming that the judge had a distant connection to Vice President Kamala Harris that posed a conflict.

In a 3-page decision dated Tuesday, the judge, Justice Juan M. Merchan, who has no direct ties to Ms. Harris, slammed Mr. Trump’s filing seeking his recusal as “rife with inaccuracies” and repetitive.

Mr. Trump’s lawyers had argued that the judge’s daughter “has a longstanding relationship with Harris” — a claim her colleagues have disputed — and cited her “work for political campaigns” as a Democratic consultant.

But prosecutors with the Manhattan district attorney’s office, which secured Mr. Trump’s conviction in May on felony charges of falsifying business records, called his request “a vexatious and frivolous attempt to relitigate” an issue that Justice Merchan had already twice dismissed.

Justice Merchan, a moderate Democrat who was once a registered Republican, rejected Mr. Trump’s initial bid to oust him last year and did so again in April, on the first day of trial. The judge cited a state advisory committee on judicial ethics, which determined that his impartiality could not reasonably be questioned based on his daughter’s interests.

Mr. Trump, who has lashed out at the judge’s family and stoked right-wing furor against his daughter, Loren Merchan, renewed the recusal request once President Biden abandoned his presidential campaign and Ms. Harris became the presumptive Democratic nominee. She is now locked in a tight race with Mr. Trump, who has falsely portrayed his conviction as a Democratic plot to foil his campaign.