“Why would you give money to a country that you think is corrupt?” Mr. Trump said.

It was one of a series of whipsawing declarations Mr. Trump made throughout the day on Monday as he defended himself, vilified the Bidens and appeared by turns eager and reluctant to reveal the facts at the root of the allegations. Mr. Trump first said he hoped that the transcript of a July 25 phone call he had with Mr. Zelensky would be released, claiming that it would exonerate him, only to angrily deny moments later that he had committed to doing so.

“I hope you get to see it soon,” Mr. Trump said, before arguing that making the transcript public would set a bad precedent — a position that one person familiar with White House deliberations said was being advanced by Secretary of State Mike Pompeo.

Mr. Biden chimed in via the president’s favorite social media platform, Twitter, responding to Mr. Trump’s dismissal of charges of misconduct by writing, “So release the transcript of the call then.”

Mr. Trump has acknowledged raising Mr. Biden and the corruption questions with Mr. Zelensky in the July 25 telephone call. People familiar with the conversation said Mr. Trump repeatedly urged his counterpart to speak with Rudolph W. Giuliani, the president’s personal lawyer, who has been pushing Ukraine aggressively to look into the Bidens and any contacts that the previous government in Kiev had with Democrats during the 2016 campaign.

Mr. Trump did not discuss the delay in the military assistance on the July 25 call with Mr. Zelensky, according to people familiar with the conversation. A Ukrainian official said Mr. Zelensky’s government did not learn of the delay until about one month after the call.

Congressional Democrats have said that if the president really pressured Ukraine for dirt on a domestic political rival, it could be an impeachable offense whether or not he tied the demand to American aid. But if evidence emerges that the president linked the two, it would most likely bolster the case of critics who call that an abuse of power.

The decision to hold back the aid, which had been approved by Congress, came at a time when the president was looking for ways to curb a variety of foreign assistance programs, and some aides at least initially saw it in that broader context. But Mr. Trump singled out Ukraine as a place he considered corrupt and railed about wasting money there, according to people who heard him discuss the matter, and he questioned the aid package for weeks.