“According to the testimony given to Congress so far, Bolton was a central figure in trying to prevent any delay in releasing foreign aid to Ukraine,” said John Yoo, a University of California, Berkeley law school professor and senior Justice Department official under President George W. Bush. “I cannot see how any responsible investigation would not seek Bolton’s appearance.”

But he added that the White House would presumably “go to the mat” to fight any effort to interview Mr. Bolton. “If the White House were to fight the House impeachment on executive privilege grounds, Bolton would be the hill on which to die,” Mr. Yoo said. “The Trump White House could claim not just that the impeachment investigation is illegitimate, which is its current line of defense, but that it is defending the right of future presidents to have an effective White House and to conduct a successful foreign policy.”

A Yale-trained lawyer, Mr. Bolton brought years of experience when Mr. Trump made him his third national security adviser in March 2018. Mr. Bolton served in both the Justice Department, where he headed the civil division under President Ronald Reagan, and the State Department, where he was an assistant secretary of state under the first President George Bush and an under secretary of state and ambassador to the United Nations under the second Mr. Bush.

While Mr. Trump appreciated his firebrand style of politics on Fox News, Mr. Bolton saw his job as keeping Mr. Trump from making unwise deals with outlier states like North Korea or Iran, leading to friction. Mr. Bolton struggled with Secretary of State Mike Pompeo for control of foreign policy and left just a day before Mr. Trump agreed to restore the frozen aid to Ukraine under pressure from Congress.

With his trademark bushy mustache and unapologetic conservative views, Mr. Bolton, 70, has built a following on the right, even flirting in the past with running for president himself. His political action committee has donated more than $1.5 million to candidates since 2014 and spent another $6 million to promote his policy views related to national security.

Since leaving Mr. Trump’s team last month, Mr. Bolton has already identified five Republican senators and congressmen for whom he plans to raise $50,000 each and, as reported by Bloomberg, sent out the solicitation email on Thursday that seemed to provide conflicting clues. He has also rejoined the Rhone Group, a private equity firm where he worked before the White House, and was spotted in South Korea in recent days talking with investors. And he is reportedly thinking about writing a book.