Following a day of trading twitter barbs, Senator Bob Corker, R-Tennessee, is firing back at President Trump again, calling into question Mr. Trump's leadership ability and his turbulent running of the White House in a New York Times report.

In an interview with the Times on Sunday, Corker said Mr. Trump was treating his office like "a reality show," with threats toward other countries that could set the U.S. "on the path to World War III."

Corker said Mr. Trump was running the West Wing "like he's doing 'The Apprentice' or something."

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"He concerns me," Corker added. "He would have to concern anyone who cares about our nation."

The new comments come after Mr. Trump lashed out at Corker on Twitter Sunday morning, saying the senator had "begged" the president to lend his support for this re-election.

Senator Bob Corker "begged" me to endorse him for re-election in Tennessee. I said "NO" and he dropped out (said he could not win without... — Donald J. Trump (@realDonaldTrump) October 8, 2017

"I said 'NO' and he dropped out (said he could not win without my endorsement)," the president noted in his Sunday morning tweet.

The president also claimed that Corker had wanted to be Mr. Trump's pick for secretary of state, "I said 'NO THANKS,'" he added, then blamed Corker as being "largely responsible for the horrendous Iran Deal."

Corker responded in a blunt response over Twitter, writing, "It's a shame the White House has become an adult day care center. Someone obviously missed their shift this morning."

It's a shame the White House has become an adult day care center. Someone obviously missed their shift this morning. — Senator Bob Corker (@SenBobCorker) October 8, 2017

According to CBS News' Margaret Brennan, Corker's chief of staff, Todd Womack, says the president's tweets paint a very different picture than what actually happened.

"The president called Senator Corker on Monday afternoon and asked him to reconsider his decision not to seek reelection and reaffirmed that he would have endorsed him, as he has said many times," Womack told Brennan in a statement on Sunday.

"I don't know why the president tweets out things that are not true," Corker told the Times. "You know he does it, everyone knows he does it, but he does."

Corker also questioned Mr. Trump's diplomacy practices, saying,"I know he has hurt, in several instances, he's hurt us as it relates to negotiations that were underway by tweeting things out."

He claimed that Mr. Trump's unpredictable leadership style has forced many senior administration officials to be on the defensive.

"I know for a fact that every single day at the White House, it's a situation of trying to contain him," Corker said.