Ukrainian police are investigating whether the US ambassador to Ukraine came under illegal surveillance by an unknown party before she was recalled from her post in May.

The announcement comes days after Lev Parnas, a former associate of Donald Trump's lawyer Rudy Giuliani, said he wanted to testify as part of the impeachment investigation into the US President.

Parnas claimed the US President "knew exactly what was going on" regarding an alleged attempt to diplomatically pressure Ukraine into investigating potential Presidential rival Joe Biden and his son - an allegation that led to Mr Trump's impeachment.

Mr Trump has dismissed the fresh allegations. Credit: AP

The former US Ambassador to Ukraine, Marie Yovanovitch, was dismissed in May.

The Ukrainian Interior Ministry, which runs the police forces, said in a statement that Ukrainian police “are not interfering in the internal political affairs of the United States”.

But the Ministry said messages published by the US House Intelligence Committee "contain facts of possible violations of Ukrainian law and of the Vienna Convention on diplomatic relations, which protect the rights of diplomats on the territory of another state."

US President Donald Trump. Credit: Steve Helber/AP

“Our goal is to investigate whether there actually was a violation of Ukrainian and international law, which could be the subject for proper reaction. Or whether it is just bravado and fake information in the informal conversation between two US citizens,” the ministry said.

The interior ministry also said it has requested the FBI provide relevant materials.

Ukrainian President Volodymyr Zelensky. Credit: AP

In another move touching on the Trump impeachment, Ukraine said it was opening an investigation into reports that Russian hackers gained access to computers of the Ukrainian gas company Burisma.

Hunter Biden, the son of Trump opponent and former US vice president Joe Biden, was on the board of that company.

The impeachment inquiry began with allegations that Mr Trump had tried to pressure Ukrainian President Volodymyr Zelenskiy into investigating Burisma by withholding promised military aid.

The FBI has been invited to take part in the Burisma hacking investigation, the ministry said.