At the time, the officials were unnerved by the removal in May of the USA ambassador to Ukraine, by subsequent efforts by Trump's lawyer Rudolph W. Giuliani to promote Ukraine-related conspiracies, as well as by signals in meetings at the White House that Trump wanted the new government in Kiev to deliver material that might be politically damaging to Democratic presidential candidate Joe Biden.
Having been made aware of this by his defence minister later, he raised the issue during a separate meeting in September in Poland with Vice President Mike Pence.
Opponents of Trump say the president used promised financial aid as leverage over the Ukrainian leader in a bid to pressure him into launching an investigation into Biden.
Trump wanted Kiev to investigate Hunter Biden's activities in Ukrainian gas firm Burisma. 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.
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".
Zelenskiy said it was "wrong" of the White House to publish a rough transcript of the call - and said he will not publish the Ukrainian transcript.
He said he "didn't even check" whether the Ukrainian transcript of the July call is the same as that of the White House, but says 'I think they match'.
While responding to Trump's requests, Zelenskiy insisted he was not his puppet, and he appeared to be trying to put an end to questions that have dogged the new Ukrainian president since details of his July 25 call with Trump emerged.
"We didn't speak about it", 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. "We have many criminal cases to look at".
The accounts are sharply at odds with Trump's depiction of the call as a "perfect" exchange in which he "did nothing wrong", despite appearing to link US support for Ukraine to that country's willingness to investigate the family of the former vice president. "And in case we need to find a solution to questions of this level, questions about our country's security, we use all our powerful possibilities". "We are an independent country".
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.
He's treading carefully to ensure continued support from the U.S. while trying to make peace with powerful neighbor Russian Federation.
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.
Trump has defended his call, saying it was "perfect" and "appropriate".