The White House's insistence that the FBI weigh in publicly about an ongoing investigation into the Trump election campaign's contacts with Russian officials is highly improper, according to former CIA Director John Brennan.

"When I was in the White House for four years, and then at the CIA, any type of engagement between the White House and the FBI about an ongoing criminal investigation was verboten [forbidden]," said Brennan, during an interview on CBS News' Face the Nation on Sunday 26 February.

The issue is especially thorny because the investigation is, in fact, looking at people who are currently senior staff members within the White House, Brennen said.

Not only is it forbidden "because of the impropriety of doing it" he added, but also because of the "appearance that it would provide to folks on the outside that there might be some unwarranted interference in such an investigation."

Brennan, who served in senior US national security positions under Presidents George W Bush and Barack Obama, urged the Trump administration to sit back and let the investigators do their work. "The White House needs to understand that the interaction with the FBI on criminal investigations is something that, really, they need to steer clear of," he said.

Last week President Donald Trump's chief of staff Reince Priebus asked a top FBI official to dispute media reports that Trump's campaign advisers were frequently in touch with Russian intelligence agents and officials during the election.

The White House also sought to enlist the help of the Republican chairmen of the Senate and House intelligence committees Senator Richard Burr (R-NC) and Representative Devin Nunes (R-CA) to quash the story. The White House maintains that the FBI told them the reports of contacts were "BS." Trump has denied there were any contacts whatsoever.

On 13 February Trump fired his national security adviser Michael Flynn after it was learned Flynn misled Vice President Mike Pence and other White House officials about his contacts with the Russian ambassador to the US. The revelation came after leaks to the New York Times and Washington Post revealed details of an FBI investigation of Flynn.

"Anybody who claims that the facts are already known in terms of what did or didn't happen between Russian officials and US persons during the election, I think, is speaking very prematurely," said Brennan.

He called for a bipartisan investigation of the communications between the Trump campaign team and Russian government officials, stating that any less would not "deliver the results that the American people need and deserve".

The current investigation in the Senate Intelligence Committee, however, is being done in a bipartisan fashion, said Senator Tom Cotton (R-AK) as he downplayed the need for an independent inquiry on Sunday on NBC News' Meet the Press.

Last week Representative Darrell Issa (R-CA) called for a special prosecutor to investigate President Trump's ties to Russia. "I think that's way, way getting ahead of ourselves here," Cotton, who sits on the Senate Intelligence Committee told NBC when asked about whether an independent investigation is needed.

"There's no allegations of any crime occurring," Cotton said. "There's not even an indication that there's criminal investigations underway by the FBI."