Mr. Tillerson said he did.

A White House spokesman, Hogan Gidley, said Thursday night that “Jared consistently follows proper protocols” with the National Security Council and State Department. He said the “alleged ‘dinner’ to supposedly discuss the blockade never happened,” and no one in the White House was “involved in the blockade.” (A transcript of the interview with Mr. Tillerson described the Riyadh meeting as a dinner.) He added that Mr. Kushner’s work with Mexico had led to positive results on trade and other issues.

The New York Times and several other news organizations obtained a copy of the committee’s interview transcript before its release on Thursday afternoon. Parts had been redacted at the request of Mr. Tillerson and the State Department.

Mr. Tillerson became secretary of state in February 2017, after being asked to meet with Mr. Trump, Mr. Kushner and two other aides, Steve Bannon and Reince Priebus, in Trump Tower. But Mr. Tillerson and Mr. Trump subsequently clashed over policy, the president’s management style and his intellectual capacity — Mr. Tillerson is said to have once called Mr. Trump a “moron” to other officials — before Mr. Tillerson was fired in March 2018.

Mr. Tillerson also alienated State Department officials and career employees because he tried to cut the budget, left important posts open and, in their eyes, remained aloof — all of which he was asked about in the committee interview.

The most telling anecdotes show Mr. Kushner and, to a degree, Mr. Bannon, making foreign policy in the shadows.

Mr. Tillerson, the former chief executive of Exxon Mobil, said that in the weeks leading up to a presidential summit in Riyadh in May 2017, Saudi officials did not give him any indication of their deepening political disputes with Qatar and their aim to join with the Emiratis and other Arab nations to impose a blockade.

One night around May 20, Saudi and Emirati leaders met with Mr. Kushner and Mr. Bannon over dinner and told the Americans of their plans for the blockade, a Democratic counsel said during the committee interview. Mr. Tillerson said he had not heard of the dinner until the committee interview.