The meeting, which has not been previously reported, came as Mr. Bolton sought to marshal Mr. Trump’s cabinet secretaries and top national security advisers to convince the president that it was in the United States’ best interest to unfreeze the funds to help Ukraine defend itself against Russia. But Mr. Bolton emerged with Mr. Trump unmoved, and instructed the aide to look for new opportunities to get those officials in front of Mr. Trump.

“The extent of my recollection is that Ambassador Bolton simply said he wasn’t ready to do it,” said the aide, Timothy Morrison, referring to Mr. Trump, according to a transcript of his testimony released by House Democrats on Saturday.

Mr. Bolton, who left the White House in September, has emerged over weeks of interviews as perhaps the single most important witness who has evaded House Democrats as they build a case that Mr. Trump abused the powers of the presidency by withholding vital military assistance and a coveted White House meeting from Ukraine until it delivered investigations he wanted. The new disclosure only makes clearer the significance of his potential testimony.