US President Donald Trump says he discussed forming a cyber security unit to guard against election hacking with Russian President Vladimir Putin.

US President Donald Trump says he and Russian President Vladimir Putin discussed forming a cyber security unit, an idea harshly criticised by Republicans who say Moscow can't be trusted after its alleged meddling in the 2016 US election.

Tweeting after his first meeting with President Vladimir Putin on Friday, Trump said now was the time to work constructively with Moscow.

"Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded and safe," Trump tweeted.

SEAN GALLUP/GETTY IMAGES US President Donald Trump's idea to form a joint cyber security unit with Russia has been panned by his fellow Republicans.

Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded.. — Donald J. Trump (@realDonaldTrump) July 9, 2017

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CARLOS BARRIA/REUTERS US President Donald Trump told his Russian counterpart Vladimir Putin it was "an honour" to hold talks with him on Friday (Saturday NZT).

Three Republican senators - Lindsey Graham of South Carolina, John McCain of Arizona and Mario Rubio of Florida - blasted the idea.

"It's not the dumbest idea I have ever heard but it's pretty close," Graham told NBC's Meet the Press programme.

"There has been no penalty," McCain, who chairs the Senate armed services committee, told CBS' Face the Nation programme.

"Vladimir Putin ... got away with literally trying to change the outcome ... of our election. Yes, it's time to move forward. But there has to be a price to pay."

Rubio, on Twitter, said: "Partnering with Putin on a 'Cyber Security Unit' is akin to partnering with (Syrian President Bashar al) Assad on a 'Chemical Weapons Unit'."

Trump argued for rapprochement with Moscow in his campaign but has been unable to deliver because his administration has been dogged by investigations into the allegations of Russian interference in the election and ties with his campaign.

Those probes are focused almost exclusively on Moscow's actions, lawmakers and intelligence officials say, and no evidence has surfaced publicly implicating other countries despite Trump's suggestion that others could have been involved.

Moscow has denied any interference, and Trump says his campaign did not collude with Russia.

Representative Adam Schiff, the top Democrat on the US House Intelligence Committee, told CNN's State of the Union programme Russia could not be a credible partner in a cyber security unit.

"If that's our best election defence, we might as well just mail our ballot boxes to Moscow," Schiff added.