Goncharuk became Ukraine's youngest-ever prime minister after Zelensky nominated him for the post in August, part of a team of fresh faces he promised would shake up the country's stagnant political scene.
Ukrainian Prime Minister Oleksiy Honcharuk said Friday he has tendered his resignation following the leak of a recording in which he is heard allegedly making disparaging comments about President Volodymyr Zelensky.
"To remove any doubts about our respect for and trust in the president, I have written a resignation letter and handed it over to the president", Oleksiy Goncharuk had written on his official Facebook page.
The press service of the Ukrainian government said it had no data about the authenticity of the recording and confirmed the premier's resignation.
Zelensky came to power promising sweeping change and has since taken several steps to resolve the separatist conflict, including prisoner exchanges and a landmark meeting with Putin in Paris last month.
According to local media reports, the participants discussed how to explain recent economic developments to Zelensky.
An alleged recording emerged earlier this week where Honcharuk questioned Zelenskiy's ability to manage the economy and the prime minister felt this would undermine his position.
On Thursday, lawmakers from the opposition party Opposition Platform-For Life demanded Honcharuk's resignation, saying he and his cabinet discredit Ukraine's president and exacerbate the economic crisis in the country.
"Zelensky has a very primitive understanding of the economy", the voice believed to be Honcharuk said, adding that he himself was a "dummy" when it came to economics.
Under Ukraine's previous president, Honcharuk's predecessor as prime minister, Volodymyr Groysman, also made threats to resign but ultimately stayed the course until last July's parliamentary election which Zelenskiy's party won.
"Zelenskiy doesn't want to dismiss Honcharuk", said Volodymyr Fesenko, head of the Penta think tank.
In the meantime, Zelenskiy called for an investigation into the source of the recording, saying, "I demand that in two weeks, as soon as possible, we obtain information on who was recording the tapes".