KIEV (REUTERS) - US Secretary of State Mike Pompeo underscored Washington's support for Ukraine on a visit to Kiev on Friday (Jan 31), as both countries sought to smooth over relations buffeted by the impeachment trial of President Donald Trump.

Ukraine was thrust centre stage in a domestic political battle in Washington last year as Trump faced down allegations that he pressured Ukrainian President Volodymyr Zelenskiy to investigate the son of his Democratic rival Joe Biden.

Pompeo has also walked back from comments that he was accused of making to a National Public Radio reporter ahead of his trip that appeared to play down Ukraine's importance to Americans.

Pompeo is the most senior US official to travel to Ukraine since the impeachment process began, and his visit comes just as Trump's impeachment trial appeared set to wrap up as early as this weekend.

"Pompeo assured Ukraine of the full support of the United States in stopping Russia's aggression and restoring Ukraine's sovereignty and territorial integrity in full," a Ukrainian statement said after Pompeo met Foreign Minister Vadym Prystaiko.

Ukraine counts on Washington for diplomatic support and military aid to buy Javelin anti-tank missiles and other hardware as it battles Russian-backed fighters in a war that has killed more than 13,000 people.

Trump temporarily froze nearly US$400 million (S$545 million) in US security assistance shortly before speaking to Zelenskiy in a July phone call, prompting accusations from Democrats he had misused US foreign policy for personal gain.

Trump's camp has called on Ukraine to investigate Biden and his son Hunter Biden, who was on the board of a Ukrainian energy company called Burisma.

Asked before the trip whether he would raise Burisma or the Bidens with Ukrainian officials, Pompeo had said: "I don't want to talk about particular individuals."

Democrats had hoped to hear from former National Security Adviser John Bolton as a witness in Trump's impeachment trial.

A report, which Bolton has not denied, said Bolton in an upcoming book has written that Trump told him he wanted to freeze military aid to Ukraine until it investigated Biden and his son Hunter.

Trump has denied any wrongdoing and called the impeachment process a "witch hunt".

Zelenskiy has denied being pressured by Trump to launch investigations and said Ukrainians were "tired" of the impeachment saga.