In a video released by Zelenskiy's office, the president called the situation "unpleasant" but said he had decided to "give a chance" to Prime Minister Oleksiy Honcharuk and his cabinet.

The furor comes at a fraught moment for Zelenskiy, who has found himself in the middle of the impeachment case unfolding against US President Donald Trump in Washington.

Trump stands accused of withholding nearly $US400 million ($A582 million) in military aid to Ukraine to pressure the country's leader to investigate Trump's political rival Joe Biden.

In a Facebook post earlier on Friday, Honcharuk praised Zelenskiy as "an example of transparency and decency to me".

"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," he wrote.

The offer to step down was subject to approval by the Rada, Ukraine's parliament. But analysts expressed doubt the resignation would come to pass.

"Zelenskiy doesn't want to dismiss Honcharuk," Penta think tank head Volodymyr Fesenko said.

Razumkov Centre think tank analyst Volodymyr Sidenko said Ukraine's president fears prompting a political crisis in the country and doesn't want to complicate his relationship with foreign investors and the International Monetary Fund.

"Honcharuk's resignation can destroy the idea of the government's unity and cast a doubt on Zelenskiy's ability to control the situation," Sidenko said.

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.

Zelenskiy is a 41-year-old former comedian whose only political experience before his election last spring consisted of playing a Ukrainian president on TV.

Australian Associated Press