Ukraine's prime minister offered his resignation on Friday after audio was leaked of him questioning President Volodymyr Zelensky's grasp of economics, in the first major political test for the inexperienced leader.

It was unclear whether Zelensky would accept Oleksiy Goncharuk's offer, which came after a recording emerged of him reportedly saying the president had a "primitive understanding" of the economy.

Zelensky, a comedian with no previous political experience, came to power after a landslide election win last year and his "Servant of the People" party later won a strong majority in parliament.

He has been embroiled in the US impeachment process and faced tough talks with Russian President Vladimir Putin, but had so far managed to avoid any significant domestic political problems.

The audio recording was leaked on social media on Wednesday and reportedly came from an informal December meeting between ministers and senior officials from the National Bank.

According to local media reports, the participants discussed how to explain recent economic developments to Zelensky.

"Zelensky has a very primitive understanding of economic processes, or rather a simple understanding," Goncharuk reportedly said on the recording, adding that he himself was an economic "ignoramus".

After initially denying reports he would step down, Goncharuk announced on his official Facebook page on Friday that he had offered to resign.

"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," Goncharuk, 35, wrote.

He did not deny making the statement, but said the audio had "artificially created an impression that my team and I do not respect the president".

"This is not true," he said. "I came to this post to carry out the president's programme."

Zelensky's office said it had received the letter of resignation and would consider it. Contacted by AFP, his spokeswoman declined any further comment.

- 'Important test' for Zelensky -

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.

The young lawyer was tasked with helping to revive an economy hit hard by corruption and Ukraine's five-year conflict with Moscow-backed separatists in the country's east.

Considered a supporter of liberal economic reforms, Goncharuk had co-founded a law firm at the age of 24 and managed an EU-funded NGO to improve the business environment in Ukraine.

Several ministers voiced support for Goncharuk after he offered to resign.

"We are a united team," Social Policy Minister Yulia Sokolovskaya said. "We support the position of the prime minister and are waiting for the decision of the president."

It will be up to parliament to eventually consider the resignation and some criticised Goncharuk for sending his letter directly to the president.

Timothy Ash, a London-based economist and expert on Ukraine, said the resignation offer was a "important test" for Zelensky.

"Removing Goncharuk for saying what he thinks... in a closed meeting, which was leaked, would I think send a very negative message to reformers," he wrote in a note.

"I think Zelensky rejects the resignation ... But this is an important test of Zelensky's reform credentials."

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.

But critics have accused him of doing little so far to boost the economy or tackle endemic corruption. And he has had to work in the shadow of the impeachment case against US President Donal Trump, who is accused of trying to pressure Zelensky into investigating political rival Joe Biden.