After a weekend of criticism of President Donald Trump's tweeted plan to create a cybersecurity unit in cooperation with Russia, the president posted on Twitter late Sunday U.S. time that he actually didn't think it would happen.

Donald J. Trump: 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!

Trump met with Russian President Vladimir Putin for the first time on Friday at the G-20 Summit in Germany.

The U.S. president claimed that he had discussed allegations that Russia interfered with the U.S. election last year, including through hacking.

But then Russian Foreign Minister Sergey Lavrov told reporters that Trump accepted Putin's assurance that Russia didn't interfere. The White House later disputed that to NBC News.

After the meeting, Trump sent a tweet saying he would work with Russia to create an "impenetrable" cybersecurity unit to keep "election hacking, & many other negative things" protected.

Donald J. Trump: Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded..

That comment, coming as pundits began referring to the G-20 Summit as the "G-19 plus one" to signal how isolated the U.S. and Trump appeared, was met with "putting the fox in charge of the henhouse" derision — referencing repeated findings by U.S. and foreign intelligence agencies that Russia was involved in wide-scale hacking campaigns.

Donald J. Trump: I strongly pressed President Putin twice about Russian meddling in our election. He vehemently denied it. I've already given my opinion.....

U.S. Sen. Lindsey Graham, a Republican representing South Carolina, mocked his president's proposed cybersecurity partnership in a weekend interview with NBC's "Meet the Press."

"It's not the dumbest idea I've ever heard, but it's pretty close," Graham said.

Administration figures had earlier defended the cybersecurity plan.

U.S. Treasury Secretary Steven Mnuchin said on ABC Sunday talk show "This Week" that the plan was "a very significant accomplishment for President Trump."

"This is a very important step forward. What we want to make sure is that we coordinate with Russia, that we're focused on cybersecurity together, that we make sure they never interfere in any democratic elections or conduct any cybersecurity [sic]," Mnuchin said. "This is like any other strategic alliance, whether we're doing military exercises with our allies or anything else."

Marco Rubio: Partnering with Putin on a "Cyber Security Unit" is akin to partnering with Assad on a "Chemical Weapons Unit".

Trump's backtrack on his cybersecurity alliance with Russia came after The New York Times reported Sunday that his son, Donald Trump Jr., met with a lawyer who had access to the Kremlin in 2016 because she may have promised information potentially damaging to Democratic presidential candidate Hillary Clinton's campaign.

The report cited three advisers to the White House briefed on the meeting and two others with knowledge of it.