"I'd find it very hard for me to sit down across the table from a guy who makes Bashar Assad look like a choir boy," Graham, a South Carolina Republican, told CNN's Kate Bolduan in reference to the North Korean leader. "If you understand what he (Kim) does to his own people, you'd be repugnant to be in the room with him."
McCain, a Republican from Arizona, told CNN's Suzanne Malveaux the President's comments were "the wrong thing to say."
"It gives some prestige to Kim Jung Un with his own people and in the world, his standing in the world, and obviously he is one of the most dishonorable people on Earth," he said. "The last remaining huge gulag in the world today resides in North Korea. So, I think it's a very unfortunate choice of words."
Graham and McCain's remarks come one day after Trump told Bloomberg News he would be "honored" to meet with Kim "under the right circumstances." White House press secretary Sean Spicer clarified the sit-down wouldn't happen until "their provocative behavior ratcheted down immediately."
McCain said Kim is "ruthless and brutal," but that the President's comments don't change "the dynamics on the ground."
Graham -- who once referred to Kim as a "nutjob" in a tweet -- urged the President to exercise caution before taking the meeting.
"If the President meets with this guy, there needs to be a purpose for the meeting," Graham said. "When you meet with somebody as president of the United States, that's the ultimate legitimacy. You provide status to that person. So I would caution meeting with anybody like this unless you had a plan."
Tension between the US and North Korea has escalated in the last few months following Pyongyang's efforts to advance its nuclear and ballistic missile programs.
"I'm sure he understands how brutal it is (in North Korea) ... it's living hell," Graham said of the country. "They are the No. 1 human rights violator in the world. Just read the UN report, it'll make you sick to your stomach."
He again emphasized Trump should not meet with Kim "unless it helps overall cause."
"(The meeting) needs to have a purpose," Graham said. "I don't understand what that purpose would be right now."
Graham also said he isn't pleased that Trump invited Duterte to the White House, who has been criticized for alleged human rights abuses, such as extrajudicial killings. But he noted "it's a tough world" and meeting with political leaders is part of Trump's job as President.
When asked about Trump's meetings with Kim and Duterte, McCain said the US has "got to return to that fundamental respect for human rights, freedom and democracy."
"It's a pillar of America ever since our beginning and particularly during the 20th century, when we were the exceptional nation," he said. "We've got to return to those principles. It doesn't mean we fight every battle, it doesn't mean engage in every conflict. It does mean we stand up for certain principles of human rights and the President, I hope, will begin to understand that."