In an all-day "media marathon" held in a Kyiv food court, Ukraine's president played down suggestions that Trump pressured him in exchange for USA military aid to help Ukraine battle Russian-backed separatists.
The complaint prompted House Speaker Nancy Pelosi to open the impeachment inquiry.
The order to move the transcript came from the White House's national security lawyers to prevent more people from seeing it, people familiar with the situation previously told CNN.
Zelenskiy scored a major political victory last month when he successfully negotiated with Putin a major prisoner exchange, which saw 70 people - some of whom were imprisoned for several years - return home in Ukraine and Russian Federation, respectively.
The US president's request that Zelensky probe the activities of Joe Biden's son Hunter has sparked an impeachment probe in the US, with the Democrats looking into whether Trump used a delayed aid package as leverage.More news: How to get new, more detailed spoken instructions from Google Maps
Then-Vice President Joe Biden arrives for a meeting with Ukrainian President Petro Poroshenko Kyiv on January 16, 2017.
Mr. Zelensky - tieless in a dark grey suit - said he would be willing to open a "joint investigation" into Burisma, the Ukrainian energy company that in 2014 hired Hunter Biden onto its board of directors. Poroshenko ousted the prosecutor based on the threat that aid would be withheld if he didn't, Joe Biden bragged a year ago. The newly-elected Ukrainian president also insisted that he didn't talk to Trump about his decision to withhold hundreds of millions of dollars in military aid from Ukraine. "We are not servants". His actions are governed by the laws of another independent country. He was speaking at an event in Kiev.
Zelensky, however, denied any allegations that President Trump attempted to "blackmail" him to open investigations, saying he didn't even know that hundreds of millions of dollars worth of USA aid had been delayed until after he spoke with Trump on July 25.
And Zelenskiy was still talking. Mr. Zelensky has been accused by Ukrainian analysts of letting Mr. Trump push him around on the call.
Zelensky emphasized that there is no corruption component in his answers to Trump.More news: Sexually transmitted disease rates continue to rise in Washington
Mr Trump has said Mr Biden did so in order to derail the inquiry into Burisma.
Asked whether the Ukrainian version matched up to the USA one, Mr Zelensky said: "I didn't even check, but I think that it matches completely".
For more than 11 hours on Thursday, Ukrainian President Volodymyr Zelensky sparred with a changing cast of journalists from Ukraine and around the world.
"I don't want to be pulled into this because I understand that my words could impact the elections of the American people", he said.
It appears to be some of these White House officials who first alerted the whistleblower who started off this process of what was going on with the July phone call and other matters related to Ukraine.More news: UAW letter to GM indicates that strike won't end quickly
Ukraine's top prosecutor, meanwhile, said on October 4 that his office is reviewing cases that were closed in the past, including cases against Burisma.