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WASHINGTON — Sen. Lindsey Graham, R-South Carolina, blasted President Donald Trump on Sunday for his administration's lack of a response to Russia's attempts to interfere in the 2016 election, saying, "This whole idea of moving forward without punishing Russia is undercutting his entire presidency."

Earlier Sunday, Trump fired off a series of tweets on his meeting with Russian President Vladimir Putin at the G-20 Summit in Germany, writing, "Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded."

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

"He gave a really good speech in Poland, President Trump did, and he had what I think is a disastrous meeting with President Putin. Two hours and 15 minutes of meetings. Tillerson and Trump are ready to forgive and forget when it comes to cyber-attacks on the American election of 2016.

"When it comes to Russia, he's got a blind spot," Graham continued. "And to forgive and forget when it comes to Putin regarding cyber-attacks is to empower Putin and that's exactly what he's doing."

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Related: Former CIA Director Brennan Says Trump 'Ceded' Ground to Putin

Graham was hardly the only Republican lawmaker to scold the president. Sen. Ben Sasse of Nebraska wrote in a Twitter post that the cyber security unit "obviously should not happen—& obviously will not happen. Why the President of the United States would tweet it is inexplicably bizarre."

This obviously should not happen--& obviously will not happen. Why the President of the United States would tweet it is inexplicably bizarre https://t.co/Y3YvnzRaku — Ben Sasse (@BenSasse) July 10, 2017

And from Sen. Marco Rubio of Florida: "Partnering with Putin on a 'Cyber Security Unit' is akin to partnering with Assad on a 'Chemical Weapons Unit.'"

Then, roughly 13 hours after his proposal, Trump apparently reversed course, again on Twitter:

"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!"

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! — Donald J. Trump (@realDonaldTrump) July 10, 2017

Trump and Secretary of State Rex Tillerson attended the meeting with Putin and Russian Foreign Minister Sergey Lavrov, with interpreters the only other people present.

U.S. intelligence agencies have concluded that Russia was behind hacks and other propaganda efforts to try to interfere with the 2016 presidential election, and NBC News has reported that senior intelligence officials believe with a "high degree of confidence" that Putin himself was personally involved.

"When it comes to Russia, I am dumbfounded," Graham said of Trump's actions. "I am disappointed and, at the end of the day, he's hurting his presidency by not embracing the fact that Putin's a bad guy who tried to undercut our democracy and he's doing it all over the world."

"He is literally the only person that I know of that has any doubt about what Russia did in 2016," he continued.

Special counsel Robert Mueller is leading an investigation into whether any associates of the Trump campaign coordinated with Russians as the Kremlin tried to interfere with the election, and Graham said he's seen no evidence of collusion.

"But the more [Trump] talks about this in terms of not being sure, the more he throws our intelligence communities under the bus, the more he's willing to forgive and forget Putin, the more suspicion," Graham said. "I think it's going to dog his presidency until he breaks this cycle."

Graham on Sunday also criticized Tillerson for the lack of hiring within the State Department, as well as a cease-fire in parts of Syria that Tillerson announced in tandem with Russia.