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.
Responding to questions from The Associated Press, Zelenskiy said he only learned after their phone call that the USA had blocked hundreds of millions of dollars in military aid to Ukraine.
USA national security officials complained about President Donald Trump's dealings with Ukraine both before his phone call with President Volodymyr Zelensky and immediately after it, The Washington Post newspaper has reported. "There was no blackmail".
The White House has published its summary of the call between Zelenskiy and Trump.
Mr Zelensky said he was open to a joint investigation into Burisma and the 2016 United States election but stressed Ukraine was an independent country with independent law enforcement agencies whose work he had no right to influence.
Zelenskiy said Ukraine would investigate because otherwise we "can't say yes or no" as to whether there was any such interference. "But it has to be confirmed", he said. "When I did find out, I raised it with [U.S. Vice-President Mike] Pence at a meeting in Warsaw", Mr. Zelensky said on Thursday.
"The absence of any clear action by Eisenberg or others may have contributed to decisions by White House insiders to relay their concerns to a CIA employee who assembled the information they supplied into a whistleblower complaint that he submitted August 12 to the US intelligence community's inspector general", the Post explains.More news: Taiwan's Tsai vows to defend island, lambasts China
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Zelenskiy said the "key question" for him was to try to persuade the White House to "change its rhetoric" about Ukraine as a corrupt and untrustworthy country.
Volodymyr Zelensky, a popular comedian before he was elected president of Ukraine this spring, promised to bring a fresh kind of politics to the ex-Soviet nation.
He said he had been made aware by his defence minister that Washington had frozen military aid to Ukraine.
"And after our meeting, America unblocked the aid".
Zelenskiy is giving an all-day "press marathon" amid growing questions about his actions as president.
"I don't want to interfere in any way in the [U.S.] elections", he said. While Mr. Zelensky acknowledged regular contacts with the oligarch - Mr. Kolomoisky's former lawyer is Mr. Zelensky's chief of staff - he said that Mr. Kolomoisky knew that Mr. Zelensky would always put the national interests first.