US President Donald Trump's choice for national security adviser, retired vice admiral Robert Harward, has turned down the offer, according to a Financial Times report.

Mr Harward was offered the job after Michael Flynn resigned on Monday for misleading Vice President Mike Pence over his conversations with Russia's ambassador to the United States.

Two sources familiar with the decision said Mr Harward turned down the job in part because he wanted to bring in his own team.

That put him at odds with Mr Trump, who had told Mr Flynn's deputy, KT McFarland, that she could stay.

At a press conference earlier today Mr Trump said Mr Flynn's actions were not wrong, but he was not happy with the way he gave information to Mr Pence.

Mr Trump said Mr Flynn was just doing his job in making a call to the Russian ambassador, but it was not acceptable that he said he could not remember the details of the call.

"I don't think he did anything wrong. If anything, he did something right," in talking to Russian officials, Mr Trump said.

"The thing is, he didn't tell our vice president properly and then he said he didn't remember."  

The White House has admitted that Mr Trump was told three weeks ago that Mr Flynn may have misled colleagues about his Kremlin contacts.

The White House had painted Mr Trump's decision as based on Mr Flynn misleading the vice president.

But it emerged on Tuesday that Mr Trump kept Mr Pence in the dark for two weeks.

The president denied allegations that members of his election campaign team were in repeated contact with Russian officials, calling it "fake news".

"They know nothing about it. They weren't in Russia. They never made a phone call to Russia. They never received a phone call. It's all fake news," he said.

He said he has asked the Justice Department to investigate intelligence leaks, calling them "criminal leaks," put out by "people in the agencies".

"We're looking at them very serious. I've gone to all of the folks in charge of the various agencies, and we're - I've actually called the Justice Department to look into the leaks."