The release of the previously confidential transcript comes as the opposition Democrats launched this week an impeachment inquiry against Trump, threatening, at the very least, to put immense political pressure on the White House ahead of elections next year.
Critics - who are demanding the release of more information, including a whistleblower complaint - immediately seized on the reconstructed transcript to say it shows that the US president was pressuring a foreign government into digging up dirt on a rival.
"Nobody pushed me," Zelensky himself said in New York as he met with Trump on the sidelines of the UN General Assembly. He added that he does not want to be "involved" in domestic US elections.
The president has lashed out, decrying "the single greatest witch hunt in American history, probably in history." The words echo Trump's language over probes into Russian interference in the 2016 election.
"There was no pressure. The way you had that built up, that call, it was going to be the call from hell, and it turned out to be a nothing call, other than a lot of people said 'I never knew you could be so nice,'" Trump said to reporters.
"I didn’t threaten anybody," Trump said. "No push, no pressure, no nothing. It's all a hoax folks."
The transcript - which can be described also as a memorandum of the call - does not show an overt and direct threat by Trump to withhold military aid, as had been alleged in some reporting, even as it revealed a discussion that will likely haunt the president.
"There's a lot of talk about Biden's son, that Biden stopped the
prosecution and a lot of people want to find out about that so
whatever you can do with the Attorney General would be great," the five-page transcript quotes Trump as saying, referring to US Attorney General William Barr.
"Biden went around bragging that he stopped the prosecution so if
you can look into it ... It sounds horrible to me," Trump is quoted as saying in the transcript, referring to an allegedly dropped probe into Biden's son.
Zelensky did promise to carry out investigations. "I guarantee as the President of Ukraine that all the investigations will be done openly and candidly," he said.
Foreign aid did come up extensively, with Trump saying the US was doing far more than European nations to help Ukraine, and Zelensky agreeing, particularly with regards to imposing sanctions on Russia over the 2014 annexation of Crimea.
"It turns out that even though logically, the European Union should be our biggest partner but technically the United States is a much
bigger partner than the European Union," Zelensky said.
Trump had insisted ahead of the release that there was "no quid pro quo" and denied any wrongdoing.
One figure who repeatedly is mentioned in the call is Trump's personal lawyer Rudy Giuliani, who has become a central figure in the saga, though his exact role is unclear, other than that he has admitted to contacting Ukraine in the affair.
Joseph Maguire, the acting director of national intelligence, will testify to Congress on Thursday about a whistleblower complaint related to the affair, which could reveal more information.
The complaint was delivered to Congress on Wednesday, a source at the Senate Intelligence Committee confirmed to dpa.
Maguire had blocked the complaint from going to Congress earlier this month, setting in motion the showdown between lawmakers and the White House.
"His administration has a well-earned reputation for dishonesty, altered facts and incomplete disclosure in public releases," Senator Chuck Schumer, the top Democrat in the Senate, said about Trump. demanding the full complaint.
Adam Schiff, a Democrat and chair of the House Intelligence Committee, likened the call to "a classic Mafia-like shakedown" and accused Trump of endangering national security.
"There is no quid pro quo necessary to betray your country or your oath of office," he said. "Ukraine knew exactly what was being asked of it."
Trump was alleged to have pressured Zelensky to provide information on possible corruption in the 2014 appointment of Biden's son, Hunter, to a senior job at Ukrainian oil and gas company Burisma.
The senior Biden has denied any wrongdoing during his time as vice president and a key US point person on Ukraine.
The call with Ukraine came just as Trump was winding down from the previous probe, by Robert Mueller, into Russian election interference in 2016. Democratic lawmakers are still investigating that affair and any obstruction of justice by Trump.
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