WASHINGTON — Senator Bob Corker, the Republican chairman of the Senate Foreign Relations Committee, charged in an interview on Sunday that President Trump was treating his office like “a reality show,” with reckless threats toward other countries that could set the nation “on the path to World War III.”

In an extraordinary rebuke of a president of his own party, Mr. Corker said he was alarmed about a president who acts “like he’s doing ‘The Apprentice’ or something.”

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

Mr. Corker’s comments capped a remarkable day of sulfurous insults between the president and the Tennessee senator — a powerful, if lame-duck, lawmaker, whose support will be critical to the president on tax reform and the fate of the Iran nuclear deal.

It began on Sunday morning when Mr. Trump, posting on Twitter, accused Mr. Corker of deciding not to run for re-election because he “didn’t have the guts.” Mr. Corker shot back in his own tweet: “It’s a shame the White House has become an adult day care center. Someone obviously missed their shift this morning.”