WASHINGTON (AFP) - Mr Joe Biden has accused Mr Donald Trump of "an overwhelming abuse of power" and called for an investigation into accusations that the United States President pressured his Ukrainian counterpart to investigate Mr Biden's son.

The presidential candidate's allegations prompted a swift rebuke from President Trump, who himself accuses the Democratic front runner of wrongdoing in Ukraine during his time as vice-president under former president Barack Obama.

The back-and-forth recriminations stem from a Washington Post report saying that a whistle-blower complaint had been filed over Mr Trump's communications with Ukrainian President Volodymyr Zelensky, and a "promise" allegedly made by the US leader.

Mr Trump allegedly pressured President Zelensky to investigate possible corruption involving Mr Biden and his son Hunter, who had worked with a Ukrainian natural gas company while his father was vice-president.

Mr Trump has urged the media to look into Mr Biden's comments in early 2016 when the then US Vice-President said the Obama administration would freeze US$1 billion (S$1.38 billion) in US loan guarantees unless Kiev fires its top prosecutor who was looking into the gas company.

"This appears to be an overwhelming abuse of power, to get on the phone with a foreign leader who is looking for help from the United States and ask about me," Mr Biden told reporters on the campaign trail in the state of Iowa.

"I know what I'm up against, a serial abuser. That's what this guy is," he continued. "If he sees any threat to his staying in power, he'll do whatever he has to do. But this crosses the line."

Mr Biden last Friday (Sept 20) demanded Mr Trump immediately release the transcript of a July 25 call with Mr Zelensky while saying that reports that the president sought to coerce his Ukrainian counterpart, if true, amounted to "clear-cut corruption".

Mr Trump slammed the allegations as ridiculous, and on Saturday accused Mr Biden on Twitter of having demanded, during his time as vice-president, "that the Ukrainian government fire a prosecutor who was investigating his son".

Mr Trump also accused news outlets of fabricating "a story about me and a perfectly fine and routine conversation I had with the new President of the Ukraine. Nothing was said that was in any way wrong, but Biden's demand, on the other hand, was a complete and total disaster".

Ukrainian Foreign Minister Vadym Prystaiko denied that there was any pressure from Mr Trump in an interview on television station Hromadske.

"I know what they were talking about and I think there was no pressure," he said.

"It was a long and friendly discussion, and it dealt with many questions that in many cases needed serious answers," he said.

Last Saturday, Mr Trump posted a video montage of media reports, which included a clip of Mr Biden saying he had asked that the prosecutor be dismissed.

Mr Biden has said the call had nothing to do with his son.

"I've never spoken to my son about his overseas business dealings," Mr Biden said. "Everybody looked at it and said there's nothing there."

He added: "Trump is doing this because he knows I'll beat him like a drum, and using abuse of power and every element of the presidency to try to do something to smear me."

Mr Biden is leading Mr Trump in most polls.

Mr Trump also excoriated media outlets whose reporting brought the alleged events to light.

"The Fake News Media nowadays not only doesn't check for the accuracy of the facts, they knowingly make up the facts. They even make up sources in order to protect their partners, the Democrats," he posted on Twitter.