Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (Texas), the No. 2 Senate Republican, said Monday that he thinks President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE should hold off on a second meeting with Russian President Vladimir Putin.

"I'm one who thinks that it's a good thing for leaders of countries to talk, but I would consider putting that one on the back burner for a while," Cornyn told reporters when asked about the White House's plans to invite Putin to the United States.

Pressed if he was saying they should wait until after the November election, Cornyn, who is a member of the Senate Intelligence Committee, reiterated that he thought the potential meeting should be sidelined "for a while."

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GOP senators have shown little enthusiasm for a second meeting between Trump and Putin after the president sparked fierce, widespread backlash for refusing to condemn Moscow's interference in the 2016 presidential election last week.

“I don’t particularly want to see a grand ceremony for Putin, but I don’t have any problem with the two leaders sitting down and hopefully having a better discourse than they’ve had until now," Hatch said, adding he hopes Trump "rethinks" his Helsinki comments.

Trump stood next to Putin after their one-on-one meeting in Finland last week and appeared to echo the Russian leader's denials that the country meddled in the 2016 election, despite the U.S. intelligence community's assessment.

"I will tell you that President Putin was extremely strong and powerful in his denial today," he told reporters during the press conference. "I will say this: I don't see any reason why it would be" Russia.

Trump tried to walk back his comments from the White House, saying he meant to say didn't see a reason it "wouldn't" be Russia. He added that he accepted the intelligence community's findings that Moscow interfered in the 2016 election.