US President Donald Trump said it would be a "positive thing" to mend US-Russia relations but says "fake reporting" is making it harder.

US President Donald Trump has gone on the defensive over his presidency, accusing America's news media of being "out of control" at a White House news conference, vowing to bypass the media and take his message "straight to the people."

Nearly a month into his presidency, Trump said he had "inherited a mess" but his new administration had made "significant progress" and took credit for an optimistic business climate and a rising stock market. He pushed back against widespread reports of a chaotic start to his administration marked by a contentious executive order - now tied up in a legal fight - to place a ban on travellers from seven predominantly Muslim nations.

"This administration is running like a fine-tuned machine," Trump declared on Thursday (Friday NZT). The president announced that he would announce a "new and very comprehensive order to protect our people."

REUTERS "I inherited a mess," US President Donald Trump said. But he was making great progress, he added.

During the news conference, Trump made a number of misstatements. He said for the third time in two days that he had won 306 Electoral College votes in his election. The correct number was 304. He called it "the biggest electoral college win since Ronald Reagan," when in fact his predecessor, Barack Obama, won 334 electoral college votes in 2012 and 365 in 2008.

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When pressed on the figures, Trump said that he meant he achieved a bigger Electoral College victory than any Republican since Reagan in 1980 and 1984 but a reporter pointed out that wasn't true either as George Bush senior brought in 426 electoral votes in the 1988 election.

When further challenged on this claim, Trump said, "I was given that information. I don't know. I was just given it. We had a very, very big margin."

He dismissed recent reports in The New York Times and CNN that the Trump campaign aides had been in contact with Russian officials before his election. Trump called Paul Manafort, his former campaign manager who has ties to Ukraine and Russia, a "respected man."

Trump called the reports a "ruse" and said he had "nothing to do with Russia." Trump added, "Russia is fake news. This is fake news put out by the media."

Amid reports of widespread leaks within his administration, Trump also warned that he would clamp down on the dissemination of sensitive information, saying he had asked the Justice Department to look into the leaks. "Those are criminal leaks," adding, "The leaks are real. The news is fake."

The president announced that Alexander Acosta, dean of the Florida International University law school and former US attorney in Florida, would be his nominee for Labour secretary. That came a day after fast-food executive Andrew Puzder withdrew after losing support among Republican senators.

If confirmed, Acosta would be the first Hispanic member of Trump's Cabinet.

Trump, a reality television star and real estate mogul who was elected as an outsider intent on change, opened a hastily arranged news conference to bash coverage by the news media. He accused reporters of not telling the truth and only serving special interests.

"The press has become so dishonest that if we don't talk about it, we are doing a tremendous disservice to the American people," Trump said.

As for his inner circle, Trump is also expected to soon name a new national security adviser following this week's ouster of Michael Flynn, who the White House said had misled Vice President Mike Pence about Flynn's contacts with Russia.

Trump is said to favour Vice Admiral Robert Harward, a former Navy SEAL, according to a White House official. Harward met with top White House officials last week and has the backing of Defense Secretary Jim Mattis. He was to meet with officials later Thursday.

Earlier in the day, Trump had a breakfast meeting with some of his staunchest House supporters.

The White House has said Trump asked for Flynn's resignation because he had misled Vice President Mike Pence over his dealings with Russia and whether he had discussed sanctions with Russia's ambassador to the US before Trump's January 20 inauguration. Flynn previously had denied those conversations to Pence and other top officials.

On Thursday, he warned in a pair of tweets that "low-life leakers" of classified information will be caught. As journalists were being escorted out of the breakfast meeting, Trump responded to a reporter's question on the subject by saying: "We're going to find the leakers" and "they're going to pay a big price."