Representative Adam B. Schiff of California, the top ranking Democrat on the Intelligence Committee, said after Wednesday’s session that Donald Trump Jr. acknowledged that he had discussed the Trump Tower meeting by telephone with his father on July 10. The congressman said that Mr. Trump’s lawyer, Alan S. Futerfas, asked the committee for more time to answer questions about that conversation because both he and a lawyer for the president were privy to it.

Mr. Schiff said that he believed the contents of the phone call should not be kept secret simply because lawyers participated in it. “The presence of counsel does not make communications between father and son a privilege,” he said. He added that he would follow up with Mr. Futerfas about the legal basis for refusing to disclose what was discussed.

Republicans on the committee who attended the session, which lasted roughly eight hours, said that they felt that Donald Trump Jr. had been forthcoming.

While he refused to recount his conversation with his father, the younger Mr. Trump told the committee about his earlier discussions with the White House adviser Hope Hicks about how to respond to the coming Times article, first published on July 8. His statement said the Trump Tower meeting was primarily about the ability of Americans to adopt Russian children. It made no mention of any promise of incriminating information from the Russian government against Mrs. Clinton.

Committee members also questioned the younger Mr. Trump at length about a series of phone calls and email exchanges that occurred several days before the Trump Tower meeting. He said that he was unable to remember a phone call that took place as he was discussing the need for the meeting with a Russian intermediary, according to three people familiar with his testimony, who spoke on the condition of anonymity to describe closed proceedings.