He added: "Helping inspire divisions because it generates support from your political base is not a formula for causing our nation to advance, our nation to overcome the many issues we have to deal with right now."
And Corker is not the only one going public with sharp criticism.
Tim Scott, one of two South Carolina GOP senators calling out the President by name Thursday -- and the sole black Republican in the Senate -- also criticized the President for his responses to the violence sparked by a Charlottesville white supremacist rally.
"I'm not going to defend the indefensible ... comments on Monday were strong," Scott told Vice News.
"His comments on Tuesday started erasing the comments that were strong. What we want to see from our president is clarity and moral authority. And that moral authority is compromised when Tuesday happened. There's no question about that."
Trump, in a series of tweets and statements over the last two weeks, has signaled that his disagreements with members of his own party continue to bother him, meaning the discord that has played out publicly shows no sign of abating. And in an unprecedented move Thursday, Trump embraced a primary challenger's attempt to unseat a sitting GOP senator, backing Kelli Ward, an Arizona state senator, over Sen. Jeff Flake.
"Great to see that Dr. Kelli Ward is running against Flake," Trump tweeted on Thursday
. "Jeff Flake, who is WEAK on borders, crime and a non-factor in Senate. He's toxic!"
The tweet is the latest sign that Trump has largely written off good relations with members of one of the chambers tasked with passing his agenda, possibly making it harder for the President to score hallmark legislative victories his White House has craved ever since Trump took office. To date, Trump's legislative wins have been thin and Republicans on Capitol Hill have said, in private that Trump's relationship with the GOP caucus is part of the problem.
While Trump has not hesitated throughout his seven-month presidency to call out members of his own party, the comments this week and the responses they inspired from his targets are a significant escalation. Even with members of Congress on recess, the legislative and executive branch have a busy agenda next month to avoid a government shutdown and avoiding a default on the national debt.
Flake, the Arizona junior senator up for re-election next year, has been notably critical of Trump. In his new book the "The Conscience of a Conservative," the senator accuses other Republicans of being in "denial" if they believe what Trump is doing is normal.
In a sign of support, Trump's public disavowal of Flake was also quickly rebuked by multiple Republicans on the Hill.
Sen. Cory Gardner, the Colorado Republican who chairs the National Republican Senatorial Committee, said in a statement that the groups tasked with protecting Senate Republican incumbents and defeating Senate Democrats still stand with Flake, despite Trump's comment.
"The NRSC unequivocally supports Senator Flake in his reelection bid," said Gardner, a senator who has been one of the most outspoken critics of Trump's response to Charlottesville.
Sen. John McCain, the senior Republican senator from Arizona, also came to Flake's defense.
Flake, McCain wrote on Twitter, "is a principled legislator & always does what's right for the people of #AZ. Our state needs his leadership now more than ever."
McCain has also been a frequent Trump target, drawing the President's ire most recently for not backing his party's plan to repeal and replace Obamacare.
During his staggering news conference on Tuesday, the same event where he blamed "both sides" for violence in Charlottesville and compared Confederate General Robert E. Lee with George Washington and Thomas Jefferson, Trump slammed McCain when a reporter asked him about one of the senator's statements.
"Senator McCain, you mean the one who voted against Obamacare," Trump asked, rhetorically. "You mean Sen. McCain who voted against us getting good health care?"
Sarcastically, Trump added: "I'm sure Sen. McCain must know what he's talking about."
Already, his strained relationships with senators have come at a cost for Republicans. When Trump's interior secretary, Ryan Zinke, called Alaska Sen. Lisa Murkowski to warn that the administration would penalize her state if she opposed Trump on health care, Murkowski dug in -- casting one of the three GOP votes that sank the Obamacare repeal effort in the Senate.
"Given how unprecedented all of this is, it's next to impossible to make concrete predictions -- except that this won't end well," said Doug Heye, a former top staffer for House Majority Leader Eric Cantor.
Earlier on Thursday, Trump singled out another GOP senator, Lindsey Graham, on Twitter after the South Carolina Republican faulted Trump's response to the Charlottesville violence.
"Publicity seeking Lindsey Graham falsely stated that I said there is moral equivalency between the KKK, neo-Nazis & white supremacists and people like Ms. Heyer," Trump wrote. "Such a disgusting lie. He just can't forget his election trouncing. The people of South Carolina will remember!"
His digital director Dan Scavino -- and the staffer who holds the keys to Trump's social media messaging -- echoed Trump.
"Publicity seeking @LindseyGrahamSC told @realDonaldTrump to come to South Carolina bc he'd 'beat his brains out' in primaries," he tweeted, adding a photo of Trump's overwhelming win in the South Carolina primary.
Graham waited little time to respond, writing in a statement that Trump is "now receiving praise from some of the most racist and hate-filled individuals and groups in our country."
"For the sake of our Nation -- as our President -- please fix this," he said.
Trump has long made known his animosity toward Flake. But he has recently given Republican senators reason to question his willingness to defend those who remain loyal to his administration as well.
In Alabama's Senate race, Trump's interests seemed to align with Senate leaders when he tweeted an endorsement and recorded a robocall for Sen. Luther Strange ahead of a Republican primary there this week.
However, when controversial former state Supreme Court chief justice Roy Moore topped Strange in the primary
, sending the two into a September runoff, Trump -- who also took credit the success Strange had -- seemed to hedge his bets, in case Moore ultimately prevails.
"Congratulation to Roy Moore and Luther Strange for being the final two and heading into a September runoff in Alabama," Trump tweeted. "Exciting race!"
Trump's attacks are not happening in a vacuum, either. Other Republicans are watching Trump savage their colleagues as he fumbles his response to an event like Charlottesville.
"I think his ability to effectively govern is dwindling by the hour," said a top Republican aide on Capitol Hill.
Heye agreed, but says the Trump currently attacking members of his party from the White House is the same Trump voters elected in November.
"Donald Trump was elected on the force of his personality, not specific policy prescriptions," he said. "So it should not be a surprise -- even when it's shocking -- that he is governing in a similar fashion."
CORRECTION: This story has been updated to add a dropped phrase back into Corker's quote.