Mr. Trump repeatedly set aside their overtures by mentioning assorted grievances he had about Ukraine, some related to efforts by some Ukrainians who backed Hillary Clinton in the 2016 election and others related to conspiracies and unsupported accusations about, among other things, a hacked server at the Democratic National Committee.

Mr. Bolton says he talked to Mr. Barr and Mr. Pompeo about Mr. Giuliani.

Mr. Bolton wrote that Mr. Pompeo privately acknowledged to him last spring that Mr. Giuliani’s claims about Marie L. Yovanovitch, then the American ambassador to Ukraine, had no basis, including allegations that she was bad-mouthing Mr. Trump. Mr. Pompeo suggested to Mr. Bolton that Mr. Giuliani may have wanted Ms. Yovanovitch out because she might have been targeting his business clients in her anti-corruption efforts. Yet Mr. Pompeo still went through with Mr. Trump’s order to recall Ms. Yovanovitch last May.

Mr. Pompeo lashed out at a National Public Radio host on Friday and Saturday after she asked him in an interview about Ms. Yovanovitch’s removal.

Mr. Bolton also wrote that he had concerns about Mr. Giuliani. He said he warned White House lawyers last year that Mr. Giuliani might have been using his work representing the president as leverage to help his private clients.

Among other names Mr. Bolton referenced in the manuscript: Attorney General William P. Barr. Mr. Bolton wrote that he raised concerns with Mr. Barr about Mr. Giuliani’s influence on the president after Mr. Trump’s July 25 call with Ukraine’s president. That call was a critical piece of the whistle-blower complaint that prompted the impeachment inquiry. Mr. Barr on Sunday denied Mr. Bolton’s account through a spokeswoman.

Mr. Bolton is willing to testify. The White House doesn’t want him to.

Mr. Bolton, who released a statement this month saying he would appear at Mr. Trump’s trial if he is subpoenaed, is prepared to testify before the Senate, according to his associates. He believes that he has relevant insight to present before senators vote on whether to remove Mr. Trump. He is also concerned, his associates said, that if his account of Mr. Trump’s Ukraine dealings comes out after the trial, he will be accused of withholding potentially incriminating material in order to increase his book sales.

Mr. Trump and the White House, however, do not want Mr. Bolton to appear.

The White House had already ordered Mr. Bolton and other key officials not to cooperate with the impeachment inquiry. The manuscript has intensified concern among advisers that they need to use a restraining order to block Mr. Bolton from testifying, according to two people familiar with their concerns. It was unclear whether they would be successful in doing so.