As political infighting continues to plague the White House, Former House Speaker Newt Gingrich says President Trump's feud with Republican Senator Bob Corker is "not helpful to the country" or "the Republican party."

"They'd be a lot better off to get together for lunch and get over it," Gingrich said on "CBS This Morning" on Tuesday.

Gingrich said that Mr. Trump "automatically hits back at anybody just as an instinctive, it goes back to his New York days and it seems to be virtually uncontrollable."

His comments come after Mr. Trump and the Tennessee senator unleashed a tit-for-tat over Twitter on Sunday, with the president saying Corker had "begged" for Mr. Trump's endorsement, saying Corker was a "negative voice" standing "in the way of our great agenda."

Corker fired back, tweeting, "It's a shame the White House has become an adult day care center. Someone obviously missed their shift this morning."

Later in an interview with the New York Times, 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."

Gingrich said that the fighting represents "the era we're in right now" as there appears to be "growing factionalization on both sides", citing Breitbart News founder Steve Bannon on the far right and Senator Dianne Feinstein on the left.

"None of them are happy with the world as it is so they're yelling about it," he said.

Gingrich also noted that Mr. Trump's angering of his own party was also detrimental to his agenda.

"I think Trump is a remarkable figure, he's a historic figure," said Gingrich, but added, "I do think there's things he doesn't understand about the American system."

The former speaker said that the biggest weakness for the two political parties "has been not finding a way to work together and the truth is the president will not get his major things done without Bob Corker."

Gingrich, who has acted as an adviser to the White House on major agenda-setting policies like health care reform and the current tax overhaul plan, says that the fighting with Corker will have implications on Republicans' efforts to provide tax cuts for America's middle class, and that it's time for the two to "move on and help the country."

"The country wants a tax cut, they need a tax cut, this is what Republicans ought to do -- talk less about each other and more about tax cuts," said Gingrich

Asked if there is anyone that could possible "reign in" Mr. Trump as he continues his tirades, Gingrich responded, "No, the president has to reign himself in."