In a Facebook post, Oleksiy Honcharuk said that he had given his resignation to President Volodymyr Zelenskiy.
"I took this post to implement the president's program. He is an example of transparency and decency to me," he said.
"However, in order to dispel any doubts about our respect and trust for the president, I have written a resignation letter and submitted it to the president for introduction to parliament," Honcharuk's statement read.
Earlier this week an audio recording surfaced in which Honcharuk appeared to make disparaging comments about Zelenskiy's understanding of economics. He called Zelenskiy "a layman" in economics and said the president should be better educated about the national currency.
Honcharuk said that the recording was a compilation of "fragments of recorded government meetings" and blamed unidentified "influential groups" for making it look like he doesn't respect the president. "It is not true," the prime minister insisted.
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. Members of the ruling Servant of the People party said there were no grounds for Honcharuk to resign.
The Rada, Ukraine's parliament, must vote on whether to accept the resignation. Zelenskiy's office confirmed that it had received the letter and said the president would take it under consideration.
Iryna Herashchenko, a lawmaker in the Rada, said that Honcharuk should have submitted his resignation to the parliament and not to the president — otherwise it doesn't bear any legal consequences and is merely "private political correspondence."
"In Ukraine, the parliament appoints the Cabinet," she argued, adding that so far the parliament hasn't received any documents related to the prime minister's resignation.
The scandal involving Honcharuk shows that different political forces have started a fight for the position of prime minister, Volodymyr Fesenko, head of the Penta think tank, told The Associated Press.
However, he added that the resignation is unlikely to be accepted: "Zelenskiy doesn't want to dismiss Honcharuk."