The U.S. House of Representatives' impeachment probe into President Donald Trump intensified on Monday, as Trump raged about the inquiry and news reports suggested he had used additional diplomatic channels to go after his adversaries.

Three House committees said a subpoena for documents had been sent to Trump's lawyer Rudy 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 Trump in the 2020 election.

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

The subpoena notes Giuliani recently said he has "evidence — in the form of text messages, phone records, and other communications" indicating he was not acting alone and that other Trump administration officials "may have been involved."

He was given until Oct. 15 to respond.

The Democratic-led House initiated an impeachment inquiry against Trump last week after a whistleblower report raised concerns that he tried to leverage nearly $400 million in U.S. aid in exchange for a political favour from Ukrainian President Volodymyr Zelensky.

U.S. Secretary of State Mike Pompeo took part in the July 25 phone call between Trump and Zelensky in which the matter was discussed, the Wall Street Journal reported, something likely to draw the attention of House investigators.

Trump meets with Ukrainian President Volodymyr Zelensky at the InterContinental Barclay New York hotel during the UN General Assembly. (Evan Vucci/Associated Press)

Two U.S. officials also told The Associated Press on Monday that Pompeo was on the call. The officials spoke on condition of anonymity to discuss an internal matter. The State Department had no comment.

The New York Times reported that Trump had sought the help of another world leader, Prime Minister Scott Morrison of Australia, with a U.S. 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, Trump asked Morrison to assist Attorney General William Barr with the probe, which Trump hopes will discredit Mueller's now-closed investigation, the Times reported.

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

An Australian government spokesperson said in an email Canberra, "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."

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.

Trump alleges 'treason'

Republican Senate majority leader Mitch McConnell appeared on Monday 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 fellow-Republican Trump.

If the House approves bringing charges, known as "articles of impeachment," against a president the process moves to the Senate which has a trial.

"I would have no choice but to take it up," 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."

Trump spent much of the day directing his ire at the Democrat leading the inquiry, suggesting on Twitter that Rep. Adam Schiff, chairman of the House intelligence committee, should be arrested for "treason."

House intelligence committee chair Adam Schiff said on Sunday he expects the whistleblower to appear before the panel very soon. (Pablo Martinez Monsivais/Associated Press)

Later, speaking to reporters at the White House, Trump accused Schiff of distorting his July 25 conversation with Ukrainian President Volodymyr Zelensky 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," Trump said.

In those comments, Schiff says the call to Zelensky "reads like a classic organized crime shakedown" and parodies the president's remarks. A spokesperson for Schiff did not respond to a request for comment on Trump's remarks.

'Entitled to anonymity'

A U.S. intelligence official filed a whistleblower complaint citing the July 25 telephone call in which Trump asked Zelensky to investigate Biden and his son Hunter, who sat on the board of a Ukrainian gas company.

The whistleblower has not been publicly identified, but Trump said on Monday that "we're trying to find out about a whistleblower. We have a whistleblower who reports things that were incorrect."

Trump has also accused the whistleblower and White House officials who gave the whistleblower information of being spies and suggested they may be guilty of treason.

"The Intel Community Whistleblower is entitled to anonymity," Andrew Bakaj, an attorney for the whistleblower, said on Twitter shortly after the president's remarks. "Law and policy support this and the individual is not to be retaliated against. Doing so is a violation of federal law."

House speaker Nancy Pelosi has said she wants to move "expeditiously" on the impeachment inquiry, perhaps paving the way for an impeachment vote on the House floor early next year.

A majority vote in favour of articles of impeachment would throw the matter to the Senate. And while McConnell said on Monday that he would be forced to hold a trial, he did not commit to letting it run its full course.

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"How long you're on it is a whole different matter," McConnell told CNBC.

According to a Senate Republican leadership aide, any senator could attempt to have the articles dismissed in the early stages of the trial, which would trigger a vote with a majority of the Senate needing to vote in favour for it to succeed.

Democrats accuse Trump of pressuring a vulnerable U.S. ally to get dirt on a rival for personal political gain. The phone call with Zelensky came after Trump froze nearly $400 million US in aid intended to help Ukraine deal with an insurgency by Russian-backed separatists in the eastern part of the country. The aid was later provided.

Schiff said on Sunday he expects the whistleblower to appear before the panel very soon.

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