U.S. President Donald Trump on Sunday backtracked on his push for a cybersecurity unit with Russia, tweeting that he did not think it could happen, hours after his proposal was harshly criticized by Republicans who said Moscow could not be trusted.

Trump said on Twitter early on Sunday that he and Russian President Vladimir Putin discussed on Friday forming "an impenetrable Cyber Security unit" to address issues like the risk of cyber meddling in elections.

The idea appeared to be a political non-starter. It was immediately scorned by several of Trump's fellow Republicans, who questioned why the United States would work with Russia after Moscow's alleged meddling in the 2016 U.S. election.

"It's not the dumbest idea I have ever heard but it's pretty close," Senator Lindsey Graham, an influential South Carolina Republican who is a member of the Senate Armed Services Committee, told NBC's Meet the Press program, saying that Trump's apparent willingness to "forgive and forget" stiffened his resolve to pass legislation imposing sanctions on Russia.

Putin 'will never be a trusted ally'

Republican Marco Rubio, who ran against Trump for the presidential nomination, tweeted: "While reality & pragmatism requires that we engage Vladimir Putin, he will never be a trusted ally or a reliable constructive partner.

"Partnering with Putin on a 'Cyber Security Unit' is akin to partnering with [Syrian President Bashar al] Assad on a 'Chemical Weapons Unit'," he added.

Ash Carter, who was U.S. defence secretary until the end of former Democratic President Barack Obama's administration in January, told CNN flatly: "This is like the guy who robbed your house proposing a working group on burglary."

Trump's advisers, including Secretary of State Rex Tillerson and Treasury Secretary Steve Mnuchin, had recently sought to explain Trump's cyber push.

Mnuchin said on Saturday that Trump and Putin had agreed to create "a cyber unit to make sure that there was absolutely no interference whatsoever, that they would work on cybersecurity together."

But Trump returned to Twitter on Sunday to play down the idea, which arose at his talks with Putin at a summit of the Group of 20 nations in Hamburg, Germany.

"The fact that President Putin and I discussed a Cyber Security unit doesn't mean I think it can happen. It can't," Trump said on Twitter.

He then noted that an agreement with Russia for a ceasefire in Syria "can & did" happen.

'Price to pay'

Republican Senator John McCain of Arizona acknowledged Trump's desire to move forward with Russia, but added: "There has to be a price to pay."

"There has been no penalty," McCain, who chairs the Senate armed services committee, told the CBS program Face the Nation. "Vladimir Putin ... got away with literally trying to change the outcome ... of our election."

Trump argued for a 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.

Special Counsel Robert Mueller is investigating the matter, including whether there may have been any collusion on the part of Trump campaign officials, as are congressional committees including both the House of Representatives and Senate intelligence panels.

trump putin composite

U.S. President Donald Trump, left, says he 'strongly pressed' Vladimir Putin twice at the G20 summit about Russian meddling in the 2016 U.S. election and that the Russian president 'vehemently denied it.' (Michael Reynolds/EPA, Alexander Astafyev/Sputnik/EPA )

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 House Intelligence Committee, told CNN's State of the Union that Russia could not be a credible partner in a cybersecurity unit.

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

Separately, U.S. government officials said a recent hack into business systems of U.S. nuclear power and other energy companies was carried out by Russian government hackers, the Washington Post reported on Saturday.

Trump said he "strongly pressed President Putin twice about Russian meddling in our election. He vehemently denied it."

He added: "We negotiated a ceasefire in parts of Syria which will save lives. Now it is time to move forward in working constructively with Russia!"

In Trump's first attempt at ending the six-year Syrian civil war, the United States, Russia and Jordan on Friday reached a ceasefire and "de-escalation agreement" for southwestern Syria.

The ceasefire was holding hours after it took effect on Sunday, a monitor and two rebel officials said.

Any joint U.S.-Russia cyber initiative would have been a different matter. Depending how much it veered into military or espionage operations, it could have faced major legal hurdles.

Language in the 2017 National Defense Authorization Act prohibits the Pentagon, which includes the National Security Agency and the U.S. military's Cyber Command, from using any funds for bilateral military co-operation with Russia.