But after it was reported that Donald Trump Jr. had been told in advance that he would be provided with incriminating information about Mrs. Clinton, he acknowledged that was the agenda for the meeting. But he said that Ms. Veselnitskaya did not provide the promised information, and instead talked about adoption policy and the Magnitsky Act.

The president has insisted that he learned of the meeting only a few days before it was first reported by The New York Times. In response to the article, Mr. Trump’s aides helped write his son’s initial statement explaining why he had met with Ms. Veselnitskaya as they flew back with the president from the Group of 20 summit meeting in Europe on Air Force One. After debating how transparent to be, the president signed off on a statement from his son that was so incomplete that it required days of follow-up statements.

Some of those briefed on the response to the initial article insisted that Donald Trump Jr. had not wanted to be forthcoming, but three people involved said that was not the case, a statement his lawyer backed on Monday.

The lawyer, Alan Futerfas, said in a statement that he and his client “were fully prepared and absolutely prepared” before the initial article on the meeting to make what he called “a fulsome statement about the nature of the meeting, what led to the meeting, what the conversation was in the meeting,” but they were overruled.