Donald Trump has dropped his plan to work with Russia to create "an impenetrable cyber security unit' soon after discussing the idea with Vladimir Putin.

The U-turn came after the two presidents had their first face-to-face meeting in Germany, and the two sides announced they had brokered a ceasefire in southern Syria that went into effect on Sunday.

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

However, the idea drew widespread ridicule and Mr Trump later tweeted: "The fact that President Putin and I discussed a Cyber Security unit doesn't mean I think it can happen. It can't - but a ceasefire can, & did!"

Senior Republican Senator Lindsey Graham of South Carolina had been among the critics, saying: 'It's not the dumbest idea I've ever heard, but it's pretty close."

He said when it comes to Russia, the president has "a blind spot" and added: "To forgive and forget when it comes to Putin regarding cyberattacks is to empower Putin and that's exactly what he's doing."

Another Senate Republican, Marco Rubio of Florida, said on Twitter: "Partnering with Putin on a 'Cyber Security Unit' is akin to partnering with Assad on a 'Chemical Weapons Unit.'"

Mr Trump's former presidential rival was referring to Syrian President Bashar Assad and his regime's use of chemical weapons against its own citizens."

Former defence secretary Ash Carter said it was "like the guy who robbed your house proposing a working group on burglary".

And Adam Schiff, the senior Democrat on the House intelligence committee, said expecting Russia to be a credible partner in any cybersecurity initiative "would be dangerously naive for this country".

Nikki Haley, the US ambassador to the United Nations, defended the idea, arguing that working with Russia on cybersecurity "doesn't mean we ever trust Russia. We can't trust Russia and we won't ever trust Russia. But you keep those that you don't trust closer so that you can always keep an eye on 'em and keep them in check."

Mr Trump said after meeting Mr Putin at the G20 summit in Hamburg that "it is time to move forward in working constructively with Russia".

But he avoided the question of whether he accepts Mr Putin's denial that Russia was responsible for meddling in the 2016 presidential election.

In a series of tweets Mr Trump said he "strongly pressed" Mr Putin twice over Russian meddling during their meeting on Friday.

Mr Trump said Mr Putin "vehemently denied" the conclusions of American intelligence agencies that Russian hackers and propagandists tried to sway the election in the tycoon's favour.

But Mr Trump would not say whether he believed Mr Putin, tweeting only that he has "already given my opinion".

Mr Trump has said he thinks Russia probably hacked the emails of the Democratic National Committee and Hillary Clinton staffers, but that "other people and/or countries" were probably involved as well.

He said before the meeting: "Nobody knows for sure."

Russian foreign minister Sergey Lavrov told reporters in Germany on Friday Mr Trump had accepted Mr Putin's assurances that Russia had not meddled.

Mr Putin said on Saturday he left the meeting thinking that Mr Trump had believed his in-person denials.

"He asked questions, I replied. It seemed to me that he was satisfied with the answers," Mr Putin said.

White House chief of staff Reince Priebus then said: "The president absolutely didn't believe the denial of President Putin."

He said Mr Trump had spent a "large part of the meeting on the subject," but wanted to move onto other topics.

Secretary of state Rex Tillerson, the only other American official in the room, said Mr Trump's conversation with Mr Putin on election meddling went "about the way we expected" and that the most important thing was to make sure it never happens again.