"We have an independent country and independent general security. I can't push anyone," Zelensky said in response to a reporter's question as he and Trump prepared to sit down for talks at United Nations headquarters in New York on Wednesday, Efe news reported.
The two presidents met after the White House released an account of a July 25 phone conversation between Trump and his Ukrainian counterpart.
A whistle-blower complaint alleging that Trump made inappropriate comments on the call led the speaker of the Democratic-controlled US House of Representatives, Nancy Pelosi, to announce Tuesday that lawmakers will begin impeachment proceedings against the president.
The White House has acknowledged that Trump put a hold on nearly $400 million in US security assistance to Ukraine about a week before the conversation in which he asked Zelensky to investigate the former vice president - now seeking the 2020 Democratic presidential nomination - and his son, Hunter.
When a reporter asked Wednesday whether he had felt any pressure from Washington to probe the Bidens, Zelensky replied: "I think you read everything. I think you read text. I'm sorry, but I don't want to be involved to democratic, open elections of USA."
"No, you heard that we had, I think, good phone call. It was normal. We spoke about many things. And I - so I think, and you read it, that nobody pushed - pushed me," the Ukrainian leader said.
"In other words, no pressure," Trump said.
The US president tried to frame his interest in the activities of Joe and Hunter Biden as a part of a broader concern about corruption in Ukraine.
"He (Zelensky) was elected - I think, No. 1 - on the basis of stopping corruption, which unfortunately has plagued Ukraine. And if he could do that, he's doing, really, the whole world a big favour. I know - and I think he's going to be successful," Trump said.
In a subsequent press conference to recap his two days at the UN, Trump called his conversation with Zelensky "perfect" and insisted the record of the call showed there was "no quid pro quo."
Critics have suggested that Trump froze the aid to Ukraine to make Kiev more amenable to his request to investigate Joe and Hunter Biden, who began serving as a paid board member of Ukrainian natural gas company Burisma Holdings in 2014 while his father was Barack Obama's vice president.
( With inputs from IANS )