The US House of Representatives' impeachment probe into President Donald Trump has intensified after a subpoena for documents was sent to Mr Trump's lawyer Rudy Giuliani.

Three House committees said the subpoena had been sent to Mr Giuliani.

The former New York mayor had said on television he asked the government of Ukraine to "target" former Vice President Joe Biden, who is seeking the Democratic nomination to run against Mr Trump in the 2020 election.

Mr Giuliani said in a tweet the subpoena raised legal issues including attorney-client privilege. "It will be given appropriate consideration," he added.

The Democratic-led House initiated an impeachment inquiry against Mr Trump last week after a whistleblower report raised concerns that Mr Trump tried to leverage nearly $400 million in US aid in exchange for investigating Mr Biden from Ukraine's leader in July.

US Secretary of State Mike Pompeo took part in the 25 July phone call between Mr Trump and Ukrainian President Volodymyr Zelenskiy in which the matter was discussed, the Wall Street Journal reported, something likely to draw the attention of House investigators.

The New York Times reported that Mr Trump had sought the help of another world leader, Prime Minister Scott Morrison of Australia, with a US Justice Department probe into the origins of what became Special Counsel Robert Mueller's investigation into Russian interference in the 2016 election.

In a recent telephone call, Mr Trump asked Mr Morrison to assist Attorney General William Barr with the probe, which Mr Trump hopes will discredit Mr Mueller's now-closed investigation, the Times reported.

"The Democrats clearly don't want the truth to come out anymore as it might hurt them politically, but this call relates to a DOJ inquiry publicly announced months ago to uncover exactly what happened," White House spokesman Hogan Gidley said in response to the Times story.

An Australian government spokesperson said in an email: "The Australian Government has always been ready to assist and co-operate with efforts that help shed further light on the matters under investigation. The PM confirmed this readiness once again in conversation with the President."

Mr Barr has held private meetings overseas with foreign intelligence officials in Britain and Italy to seek their assistance as well with that investigation, the Washington Post reported.

In the Giuliani document request, the chairmen of three House committees said he had "stated more recently that you are in possession of evidence - in the form of text messages, phone records, and other communications - indicating that you were not acting alone and that other Trump Administration officials may have been involved in this scheme."

He was given until 15 October to respond.

Republican Senate Majority Leader Mitch McConnell has appeared to put to rest speculation he would use his position to derail any impeachment effort by the Democratic-led House by avoiding a trial at all.

The Republicans control the Senate and have been largely muted about the allegations and inquiries into Mr Trump.

If the House approves bringing charges, known as "articles of impeachment," against a president, the process moves to the Senate, where there would be a trial.

"I would have no choice but to take it up," Mr McConnell told CNBC.

"Under the Senate rules, we are required to take it up if the House does go down that path. "The Senate impeachment rules are very clear."

Mr Trump spent much of the day directing his ire at the Democrat leading the House inquiry, suggesting on Twitter that US Representative Adam Schiff, chairman of the House Intelligence Committee, should be arrested for "treason."

Later, speaking to reporters at the White House, Mr Trump accused Mr Schiff of distorting his conversation with Mr Zelenskiy at a House hearing last week.

"Adam Schiff made up a phony call and he read it to Congress and he read it to the people of the United States and it's a disgrace," Mr Trump said.

In those comments, Mr Schiff said the call to Mr Zelenskiy "reads like a classic organised crime shakedown" and parodied the president's remarks.