The President had earlier accused Corker, who is retiring, of blocking his party's efforts on tax cuts.
The exchange between the two men escalates a rift that has highlighted divisions between Trump and several Republican lawmakers, threatening to send the President off-message at a critical time for his agenda.
Corker, asked in the interview if he should have backed Trump's presidential campaign, said he "would not do that again." He also said Trump has "great difficulty with the truth" and that "debasing" the US would be his prime legacy as President.
"You wouldn't support him again?" Raju asked.
"No, no way," Corker said.
Corker said Trump has "proven himself unable to rise to the occasion."
"I think many of us, me included, have tried to, you know, intervene, and I have had a private dinner and have been with him on multiple occasions to try and create some kind of aspirational approach, if you will, to the way that he conducts himself," Corker said. "I don't think that that's possible. He's obviously not going to rise to the occasion as president."
Asked if he thought the President was a role model for children, Corker, the chairman of the Senate foreign relations committee, said, "No, absolutely not."
"I think the things that are happening right now that are harmful to our nation, whether it's the breaking down of -- we are going to be doing hearings on some of the things that he purposely is breaking down -- relationships we have around the world that have been useful to our nation," he said. "But I think at the end of the day, when his term is over, I think the debasing of our nation, the constant non-truth telling, just the name-calling ... I think the debasement of our nation will be what he'll be remembered most for, and that's regretful."
Corker also declined to answer if he trusts Trump to handle the nuclear codes, and later told reporters "I've seen no evolution" from Trump.
After the CNN interview aired, Trump on Twitter called Corker "the incompetent head of the foreign relations committee." Corker later said "everybody sees through" Trump's "bullying."
Trump attended a lunch with lawmakers he spent much of the summer blasting for failing to enshrine his political agenda. Some have been critical over his chaotic, unpredictable method of governing, but Trump hoped to woo them to finally rack up a key legislative win on tax reform. Senators who attended the lunch said the President's feud with Corker wasn't brought up
House Speaker Paul Ryan said at a news conference later Tuesday morning that he didn't think the Trump-Corker spat would affect Republicans' efforts on tax reform.
"I know Bob, who supported the budget, wants to get tax reform. I know the President want to get tax reform," Ryan said. "I'm glad the President is coming to lunch, because I've have long believed it's best to settle these things in person and I hope that they can get a chance to do that."
Ryan said he believes Corker will vote for the GOP's tax plan. But Rep. Chris Collins, R-New York, told CNN that Republicans didn't necessarily need Corker's support, noting that the party only needs 50 votes from its 52-seat caucus to pass its tax plan, with Vice President Mike Pence able to cast a tie-breaking vote -- to hit the necessary 51 -- if necessary.
"He should be embarrassed," Collins added, referring to Corker.
Insults exchanged over Twitter
In a series of tweets earlier Tuesday, the President accused Corker of fighting tax cuts and called him a "lightweight." Corker responded by again likening the White House staff to a daycare center.
"Bob Corker, who helped President O give us the bad Iran Deal & couldn't get elected dog catcher in Tennessee, is now fighting Tax Cuts....," Trump tweeted. "...Corker dropped out of the race in Tennessee when I refused to endorse him, and now is only negative on anything Trump. Look at his record!"
Corker soon responded on Twitter: "Same untruths from an utterly untruthful president. #AlertTheDaycareStaff."
Corker had criticized Trump during appearances on several television shows Tuesday morning.
On NBC, Corker called Trump's effort to court senators over the White House's tax reform proposal "a photo-op." And speaking to ABC, he suggested that the President butt out of the process.
"(I)f you start taking things off the table before you get started you make that very difficult. So what I hope is going to happen is the President will leave this effort, if you will, to the tax writing committees and let them do their work and not begin taking things off the table that ought to be debated in the committees at the proper time," he said on "Good Morning America."
When asked if the President is a national security threat, Corker told NBC that he needs to be contained by members of his Cabinet, namely, Secretary of Defense James Mattis, Secretary of State Rex Tillerson, and White House chief of staff John Kelly.
Both Trump and Corker -- who was once in consideration
to become Trump's secretary of state -- have publicly bickered
following the Tennessee senator's announcement earlier this month that he would not be seeking a third term in the Senate.
Trump attacked Corker via Twitter at the time, saying he denied the senator's request for an endorsement -- a claim denied by Corker's office. In response, Corker said
, "It's a shame the White House has become an adult day care center. Someone obviously missed their shift this morning."
In remarks to a New York Times story published a short time later, Corker said Trump was treating the presidency like "a reality show," making reckless threats against other countries that put the United States "on the path to World War III."