By Monday morning, Senator Mitch McConnell, Republican of Kentucky and the majority leader, and Mr. Graham had pressed the White House for an explanation of Mr. Bolton’s account.

Stephanie Grisham, the White House press secretary, said that Mr. Bolton's manuscript was provided to the National Security Council and edits to it had not been seen or made by anyone else in the White House.

“That is something that we have kept walled off for obvious reasons,” Ms. Grisham said Monday on Fox News. “Just could be a conflict with the trail going on, so it’s nothing that I’ve seen and nothing that I know about in terms of what they would remove for national security.”

Fred Fleitz, Mr. Bolton’s former chief of staff, called on him in an opinion piece for Fox News to immediately withdraw the book from the publisher.

Mr. Bolton’s lawyer blamed the White House for the disclosure of the book’s contents, which Mr. Bolton submitted for a standard security review 12 days after the House impeached Mr. Trump. It is possible that the submission of Mr. Bolton’s book to the White House deepened desires to keep Mr. Bolton from testifying.

In his manuscript, Mr. Bolton describes an effort that he had made, along with Secretary of State Mike Pompeo and Defense Secretary Mark T. Esper, to push Mr. Trump to release the aid. Mr. Bolton said he also spoke with Attorney General William P. Barr about his concerns over the parallel diplomacy with Ukraine led by the president’s personal lawyer, Rudolph W. Giuliani. Mr. Barr, whom Mr. Trump mentioned in his July phone call with Mr. Zelensky, has tried to distance himself from Mr. Giuliani and the Ukraine matter.

Bob Driscoll, a lawyer for Mr. Mulvaney, disputed Mr. Bolton’s account and said Mr. Bolton was merely trying to sell his book, which is set to be released in mid-March.

Mr. Bolton, who has said he would testify at the Senate trial if he was subpoenaed, wrote in the manuscript that Mr. Pompeo told him privately that there was no basis to criticize the American ambassador to Ukraine at the time, Marie L. Yovanovitch. Career diplomats have testified that there was no justification to fire Ms. Yovanovitch. Mr. Giuliani and two of his associates had been pushing Mr. Trump to fire her since the spring of 2018.

Maggie Haberman contributed reporting.