GOP senators criticize Trump's overtures to controversial leaders

The leaders include Turkey's Erdogan, the Philippines' Duterte and Kim Jong Un.

Corker suggested he was concerned about all such communications, including to Duterte and Kim, but specified that the phone call congratulating Erdogan on the April vote that substantially consolidated his power "had a very damaging effect" with America's allies.

On the invitation extended to Duterte to visit the White House, Corker said, "I think the president sometimes is being conversational and trying to show an openness and I think as time goes on he'll understand the gravity of actually having people come to the White House like that."

"[Duterte] is certainly not on the list of people that I would want to be one of the first people to come visit," Corker added.

McCain, the Senate Armed Services Committee chairman who has shown a willingness to critique the president -- who once addressed McCain's stay in a Vietnamese prisoner of war camp by saying, "I like people who weren't captured" -- also criticized Trump's overtures to authoritarian leaders around the globe.