A federal judge in Manhattan denied an effort by Donald J. Trump to move his already adjudicated state criminal case to the federal courts on Tuesday, rejecting his claims of bias against him as well as his claims of presidential immunity.

In late May, a jury convicted the former president on 34 felony counts of falsifying records to cover up hush-money payments to a porn star, Stormy Daniels, who had threatened to go public with her account of an affair. A state judge, Juan M. Merchan, has scheduled his sentencing for Sept. 18, though Mr. Trump has asked him to delay it until after the presidential election.

In a four-page decision on Monday, Judge Alvin K. Hellerstein of Federal Court in Manhattan said he could not evaluate Mr. Trump’s claims of bias, saying those were issues for the state courts. But he said that Mr. Trump’s claims of immunity for official acts — based on a recent Supreme Court decision affirming such protection — were irrelevant in this case.

He noted that “hush-money payments were private, unofficial acts, outside the bounds of executive authority.”

This is a developing story and will be updated.