“I’m leading in the polls and they have no idea how to stop me,” Mr. Trump said, addressing reporters minutes he spoke at the United Nations gathering. The president trails the leading Democratic candidates in most polls. “The only way they can try is through impeachment,” he added.

The $391 million aid package in question was provided to Ukraine for its defense against a Russian-backed separatist insurgency in its east which has left more than 13,000 people dead over the past five years.

Mr. Trump also noted that the funds allocated for Ukraine “were fully paid,” although he did not mention the fact that his administration acted only after the delay became public through news media leaks, and under bipartisan pressure from Congress.

He also did not mention that he had changed his explanation for withholding the money from just a day before. On Monday, he linked his decision to block the aid to his concerns about corruption in Ukraine, citing Mr. Biden as an example. By emphasizing instead his overall concern about foreign aid, he was advancing a rationale less tied to his demand for an investigation.

Mr. Trump earlier repeated his assertion that the transcript would exonerate him.

“When you see the call, when you see the readout of the call, which I assume you’ll see at some point, you’ll understand that call was perfect,” he said.

In a brief interview with Voice of America’s Ukrainian outlet, Mr. Zelensky said he expected continued support from the United States and predicted that a meeting he is scheduled to have with Mr. Trump at the United Nations on Wednesday would “be very warm.”

“We just want the U.S. to always support Ukraine and Ukraine’s course in its fight against aggression and war,” Mr. Zelensky said at the United Nations. “It seems to me that it is so. And everything seems to lead to this.”