July 9 (UPI) -- President Donald Trump said Sunday he wants to "move forward in working constructively with Russia," including forming a cybersecurity unit between the two countries -- an idea that drew immediate scorn from several Republican senators.
On Sunday, one day after arriving in Washington from the G20 summit in Germany, Trump posted on Twitter: "Putin & I discussed forming an impenetrable Cyber Security unit so that election hacking, & many other negative things, will be guarded."
Trump, in another tweet, said he "strongly pressed" Putin twice about Russian meddling in the election during their Friday meeting in Germany and that Putin "vehemently denied it." The two-hour session was their first face-to-face meeting with Trump as president.
Trump noted the two nations worked together on a cease-fire in Syria but Russian sanctions won't be lifted "until the Ukranian & Syrian problems are solved." He was referring to Russia's intervention in Ukraine.
Tillerson, speaking to reporters Sunday while traveling to Kiev, Ukraine, said the two nations agreed "to explore a framework under which we might begin to have agreement on how to deal with these very complex issues of cyberthreats, cybersecurity, cyber intrusions."
The United States faces cyberthreats from many countries, he said, adding: "This is a challenge, obviously, for us globally."
Nikki Haley, the U.S. ambassador to the United Nations, said working with Russia on cybersecurity will "keep them in check."
"It doesn't mean we've ever taken our eyes off of the ball," she said on CNN's State of the Union. "It 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 them."
Sen. Lindsey Graham, R-S.C, said that partnering with Russia on cybersecurity is "not the dumbest idea I've ever heard, but it's pretty close."
"When it comes to Russia, he's got a blind spot," Graham said on NBC's Meet the Press. "To forgive and forget when it comes to Putin regarding cyberattacks is to empower Putin, and that's exactly what he's doing."
And former defense secretary Ashton B. Carter, who served under President Barack Obama, also had a pointed response. He said on State of the Union, "When confronted with something wrong, they ask for U.S. intelligence -- old trick -- and propose a working group, in this case on cyber. But this is like the guy who robbed your house proposing a working group on burglary."
The White House said Sunday that Trump did not believe Putin's denials of their meddling in the U.S. presidential eletion.
"This was not just a five-minute piece of the conversation. This was an extensive portion of the meeting and after going at it with President Putin more than once, two times, maybe even three times, the president at that point, after spending a large part of the meeting on the subject, moved on to other topics."
Trump in his tweets said only, "I've already given my opinion."
During news conference Thursday in Warsaw, Poland, Trump said: "I think it could very well have been Russia, but I think it could well have been other countries."
"Nobody really knows for sure," he added.