President Donald Trump's choice for national security adviser, retired Vice Admiral Robert Harward, has rejected the job.

Harward was offered the job after Michael Flynn was fired by Trump on Monday for misleading Vice President Mike Pence over his conversations with Russia's ambassador to the United States, AAP reports.

A White House official said on Thursday Harward cited family and financial reasons for opting not to take the job. Harward is a senior executive at Lockheed Martin.

One senior U.S. official said that "family considerations changed his mind." A friend of Harward's added the former Navy SEAL was also not fully comfortable with the quickly moving process. All requested anonymity to discuss the sensitive matter, Washington Post reports.

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

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

The administration had hoped to name Harward to the position this week, in an effort to soothe the turmoil rolling through the White House. Even before Flynn resigned, the administration was quietly wooing Harward.

The hard-charging former Navy SEAL was at the White House on February 8 and then again this week, according to an administration official. Harward commanded high-risk operations in Iraq and Afghanistan and later parachuted into his own retirement ceremony from high altitude.

Trump appeared to refer to Harward earlier in the day at a presidential news conference, saying: "I have somebody that I think will be outstanding for the position."

The president also made clear why he asked Flynn to resign, saying it was because the retired lieutenant general had not been completely truthful with Pence about his conversations with the Russian ambassador to the United States, Sergei Kislyak.

"The thing is, he didn't tell our vice president properly, and then he said he didn't remember. So either way, it wasn't very satisfactory to me," Trump said.

Harward's decision not to take the job leaves the White House scrambling to find a leader for the security council, which is struggling to get its bearings.

Most NSC staffers are traditionally on temporary duty from the Defense and State departments and the intelligence agencies, but as many as 60 slots are vacant, according to senior officials who denied reports that the White House was having trouble recruiting to fill them. They said the vacancies are due to rotational and turnover delays in what are normally two-year assignments.

The White House hires about 75 of a total of more than 200 staffers on the council. The staff chosen by Flynn is heavily weighted toward the small world of military intelligence officials or strategists who rotated through Iraq and Afghanistan with him over the past decade.

- AAP, Washtington Post