Ukrainian President Volodymyr Zelensky said on Tuesday that his country is "tired" of questions related to the Trump scandal, amid a critical week of public impeachment hearings in Washington.

"We have our country, we have our independence, we have our own problems," he complained after a press conference in Kiev with visiting Czech prime minister Andrej Babis.

Hearings began last week in Washington into whether US President Donald Trump ordered to freeze US military aid to Ukraine in an effort to get Kiev to launch investigations against potential 2020 election rival Joe Biden and his son Hunter.

On Tuesday an American reporter pressed Zelensky on whether he had been ready to launch a probe into Biden's son's ties to Ukraine energy company Burisma, as a concession to Trump.

"Everyone in Ukraine is so tired of Burisma," Zelensky said, before quickly leaving the room full of reporters.

Zelensky, a 41-year-old comedian who was elected President of Ukraine in April, has found himself at the centre of the impeachment scandal in the US after his phone call with Trump resulted in a probe into whether the US president had pressured his Ukrainian counterpart to further his own personal agenda.

The Ukrainian probe was to target Hunter Biden's activities from April 2014 to April 2019 when he served on the board of Burisma Holdings, a Ukrainian gas firm accused of corrupt practices.

The global attention on the affair has come at a time when Ukraine is trying to enact crucial reforms, and Zelensky has shown exasperation with the relentless media focus on Trump.

At a marathon press-conference last month, Zelensky said he does not want to "get sucked into" the scandal as it could hurt Ukraine's interests.

"With all due respect for the US and US politics, we are not maintenance staff for the US, we're an independent country," he said.

US is a key ally of Ukraine in its long-running fight against Russia-backed separatists in the east.