Ukrainian authorities have opened an investigation into illegal gambling allegations against former prosecutor general Yury Lutsenko, who repeatedly met with Rudy Giuliani as Donald Trump's lawyer tried do dig up dirt in Ukraine on Joe Biden.

The state investigations bureau said on Tuesday it had opened a criminal case into potential abuse of office against Mr Lutsenko following a complaint by the chairman of president Volodymyr Zelenskiy's Servant of the People party, which won a parliamentary majority in July.

The bureau said Mr Lutsenko was accused of a “premeditated conspiracy” with former parliamentarians related to an illegal gambling business.

The case comes just days after impeachment proceedings were begun against Mr Trump for allegedly pressuring Mr Zelenskiy to investigate Hunter and Joe Biden over suspicions believed to have been encouraged by Mr Lutsenko.

The Bidens have denied any wrongdoing.

Mr Zelenskiy has tried to distance himself from the impeachment process, again denying on Tuesday that Mr Trump pressured him by withholding military aid.

Mr Lutsenko went to the UK to study English this week. On Facebook, he said investigators had a “big imagination” to accuse him of such things, arguing that his income had been thoroughly checked.

Mr Lutsenko said this week he had told Mr Giuliani he would cooperate if the United States opened an investigation, but pushed back on demands to investigate them himself, as they had not broken any laws.