If Mr. Trump had tried to assert executive privilege and the Senate committee challenged him in court, legal experts said, Mr. Trump had a weak case because he has himself publicly discussed his private conversations with Mr. Comey.

“The president’s power to assert executive privilege is well established,” Sarah Huckabee Sanders, a White House spokeswoman, told reporters. “However, in order to facilitate a swift and thorough examination of the facts sought by the Senate Intelligence Committee, President Trump will not assert executive privilege regarding James Comey’s scheduled testimony.”

The president fired Mr. Comey on May 9 as the F.B.I. was looking into contacts between Russia and Mr. Trump’s associates. While Mr. Trump and his aides initially said he had acted at the recommendation of the deputy attorney general because of the way Mr. Comey handled last year’s investigation into Hillary Clinton’s emails, Mr. Trump later said that he had already decided to fire the F.B.I. director regardless of any recommendations and that he had the Russia investigation in mind.

In the weeks since, associates of Mr. Comey have said the former director felt uncomfortable about efforts by Mr. Trump to compromise the bureau’s traditional independence. Just days after Mr. Trump’s inauguration, he invited the director to dinner and, according to people familiar with Mr. Comey’s account, asked him repeatedly for his loyalty, which Mr. Comey declined to give. Mr. Trump has denied that he did so, but he said it would not have been wrong if he had.

A few weeks later, the day after Mr. Trump pushed out Michael T. Flynn, his national security adviser, who had provided misleading accounts of a phone call with Russia’s ambassador, the president asked Mr. Comey to drop the investigation into Mr. Flynn, according to notes taken contemporaneously by Mr. Comey and read to a New York Times reporter. Mr. Comey refused.