Mr. Morrison’s testimony added a portrait of how of Mr. Bolton has worked feverishly to ensure the regular interagency policymaking of the executive branch prevailed over an irregular policy channel that appeared meant to serve Mr. Trump’s personal political interests. That channel included the United States’ ambassador to the European Union, the president’s private lawyer and a handful of others pressing Ukraine to commit to investigations of former Vice President Joseph R. Biden Jr. and a debunked conspiracy theory about Ukraine and the 2016 election.

In his testimony, Mr. Morrison said that Mr. Bolton advised him to be wary of the president’s irregular policymaking channel, including the envoy to the European Union, Gordon D. Sondland.

“My consistent direction from Ambassador Bolton was, ‘Do not get involved, and make sure the lawyers are tracking,’” Mr. Morrison said, referring to Mr. Sondland and the efforts he was involved in. Mr. Morrison’s predecessor as the National Security Council’s senior director for Russia and Europe told investigators that Mr. Bolton issued a similar instruction after a run-in with Mr. Sondland, who will testify publicly himself next week.

Mr. Morrison’s testimony made clear that he and Mr. Bolton were deeply skeptical of Mr. Sondland, a wealthy hotelier and political donor turned ambassador. He said he suspected Mr. Sondland’s stated influence with the president might be exaggerated. Following Mr. Bolton’s directions, he reported interactions he had with the ambassador to White House lawyers. But when he followed up, Mr. Sondland seemed to be telling the truth and appeared to have Mr. Trump’s ear on Ukraine matters.

“Ambassador Sondland believed and at least related to me that the president was giving him instruction,” Mr. Morrison testified.

Mr. Morrison described witnessing Mr. Sondland approach an aide to Mr. Zelensky during a high-level meeting in Warsaw in September. The conversation took place just after a meeting in which Mr. Pence assured Mr. Zelensky that the United States still fully supported Ukraine and would decide on the security aid soon. The vice president did not mention the investigations during the meeting, Ms. Williams said.

Mr. Sondland was blunter, though, he later told Mr. Morrison. He told Mr. Zelensky’s adviser that “what could help them move the aid was if the prosecutor general would go to the mic and announce that he was opening” the investigation Mr. Trump wanted.