A TV and film comedian, Zelenskiy overwhelmingly won the presidency in April on promises to fight corruption and end the five-year conflict with Moscow-backed separatists in eastern Ukraine.
A whistleblower's report filed with the inspector general of the intelligence community first revealed the phone call, and the White House released a rough transcript of the conversation between the two leaders.
He flipped from Ukrainian to English and Russian.
Asked if Ukraine should also probe the Bidens, the president affirmed: "I would think that if they were honest about it, they would start a major investigation", before adding, "Nobody has any doubt that they weren't crooked; that was a crooked deal, 100 percent". Stubble poked through his cheeks.
In Donetsk, separatist commander Ruslan Yakubov told the DAN News website that the rebel forces were ready for the pullback but did not go ahead because Kyiv did not indicate its readiness.
Ukraine's president has denied that Donald Trump tried to "blackmail" him into starting an investigation linked to candidate Joe Biden, but said he would help the United States if it opened its own investigation. He said he couldn't "say yes or no" as to whether there was interference.
Zelensky said he does not intend to release the Ukrainian transcript of his phone call with President Trump. As the scandal has unfolded, an obvious quid pro quo has come into focus: Ukraine needed military aid; Trump wanted something he could use to defeat Joe Biden; and the Republican hoped to trade one for the other.
Zelensky said he wasn't even aware that almost $400 million was being held up when he spoke to Trump on July 25.
But Zelenskiy insisted he's not Trump's puppet and his moves appeared to be an attempt to put an end to questions dogging the Ukrainian president since details of his July 25 call with Trump emerged.
Volodymyr Zelenskiy said for the first time that his country will "happily" investigate the conspiracy theory pushed by Trump that it was Ukrainians, not Russians, who interfered in the 2016 USA presidential election.
"This is not corruption, it was just a call", Mr Zelensky said on Thursday.
At least four national security officials were so alarmed by the Trump administration's attempts to pressure Ukraine for political purposes that they raised concerns with a White House lawyer both before and immediately after President Trump's July 25 call with that country's president, according to US officials and other people familiar with the matter.
Mr. Zelensky said on Thursday that he had felt no pressure and "no blackmail" during his conversation with Mr. Trump - an answer that Mr. Trump immediately posted on his Twitter account, claiming it exonerated him.
Zelenskiy is giving an all-day "press marathon" amid growing questions about his actions as president.