Former Speaker Newt Gingrich (R-Ga.) on Tuesday said he doesn't think President Trump's feud with Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.) is good for the country or for the GOP.

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

Gingrich said Trump automatically hits back at anybody as an instinct.

"It goes back to his New York days, and it seems to be virtually uncontrollable," Gingrich said.

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"And he thought that Corker said something that had offended him so he hit Corker, so Corker, who's now liberated, hit him back," he continued.

"I think it's not helpful for the country, it's not helpful to the Republican Party."

Gingrich was pressed on how angering members of his own party would help the president with his efforts to get tax reform done.

"It doesn't," Gingrich said.

The former Speaker said he thinks Trump is a "remarkable figure," but he added: "I do think there are things he doesn't understand about the American system."

The president will not get his major agenda items passed without Corker, Gingrich said.

When asked if anyone could rein in the president, Gingrich said: "No, the president has to rein himself in."

Trump in recent days has escalated his feud with Corker.

This past weekend, Trump took aim at Corker on Twitter, saying the Tennessee Republican begged him for his endorsement but that he declined the request.

Corker, who announced he is not running for reelection, shot back, saying the White House had turned into "an adult day care center."

In a New York Times interview, Corker then said Trump's threats to other countries could put the U.S. "on the path to World War III."

On Tuesday, in a tweet that happened after the Gingrich interview, Trump again targeted Corker, saying The New York Times had set Corker up by recording him.

"The Failing @nytimes set Liddle' Bob Corker up by recording his conversation," Trump tweeted Tuesday. "Was made to sound a fool, and that's what I am dealing with!"