"This is not corruption, it was just a call," Mr Zelensky said on Thursday.
The call prompted a whistleblower complaint and Democratic impeachment inquiry of the Republican president.
Mr Trump denies withholding US aid while pressuring Ukraine to investigate political rival Joe Biden.
Impeachment is a process by which Congress can vote to oust a president - though it requires support from a majority of both chambers and as such, is currently thought unlikely to pass the Republican-controlled Senate.
Speaking to reporters at a news conference in Kiev on Thursday, Mr Zelensky said of his 25 July call with Mr Trump: "There was no blackmail. It was not the subject of our conversation."
He said the purpose of the conversation was to arrange a meeting with Trump, and there were no "conditions" from the American side.
Mr Zelensky also said he does not believe US-Ukraine relations will be affected by the impeachment inquiry.
A rough transcript of the call released by the White House shows Mr Trump asked Mr Zelensky to investigate Joe Biden, now a Democratic frontrunner for next year's White House election.
His son, Hunter Biden, landed a lucrative board position in 2014 with a Ukrainian gas firm, Burisma, that found itself under scrutiny from a former prosecutor general.
As US vice-president Mr Biden, like other Western officials, put pressure on Ukraine in 2016 to have the prosecutor fired, citing corruption concerns.
Mr Trump has said Mr Biden did so in order to derail the inquiry into Burisma. Ukrainian officials have said there is no evidence of wrongdoing by the Bidens.
The whistleblower who filed a complaint over the call said in a memo that a White House official who listened to the phone discussion described it as "crazy" and "frightening", US media report.
The official was "visibly shaken by what had transpired" in the call, the whistleblower reportedly wrote in the memo.
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