Republican Sen. John Kennedy (R-La.) said Sunday that Environmental Protection Agency (EPA) Administrator Scott Pruitt Edward (Scott) Scott PruittJuan Williams: Swamp creature at the White House Science protections must be enforceable Conspicuous by their absence from the Republican Convention MORE should face the press amid his mounting controversies.

“I would do a full blown press conference and say 'OK here are your criticisms. That's fair. I'm going to stop doing it. Here's what I think is not fair,’ ” Kennedy told CBS’s “Face the Nation” of Pruitt.

“But these people are hurting the president and I'm not saying he's not a good person," he added. "But the appearance of impropriety matters.”

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The embattled EPA head has been under intense scrutiny over his reported relationship with lobbyists and use of taxpayer funds for matters like security and travel.

But President Trump Donald John TrumpBubba Wallace to be driver of Michael Jordan, Denny Hamlin NASCAR team Graham: GOP will confirm Trump's Supreme Court nominee before the election Southwest Airlines, unions call for six-month extension of government aid MORE has insisted Pruitt “is doing a great job.”

“While security spending was somewhat more than his predecessor, Scott Pruitt has received death threats because of his bold actions at EPA,” Trump said Saturday evening.

Kennedy said it’s up to Trump as to whether Pruitt should retain his Cabinet position, but that the continued missteps need to end.

“There are a lot of problems we can't solve. But you can behave. I'm not— I don't mean to denigrate Mr. Pruitt but doggone it he represents the president of the United States and it is hurting his boss and it needs to stop,” Kennedy said.

Other Republican senators have also expressed concern over Pruitt's scandals, including Sen. Lindsey Graham Lindsey Olin GrahamGraham: GOP will confirm Trump's Supreme Court nominee before the election Fox's Napolitano: Supreme Court confirmation hearings will be 'World War III of political battles' Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee MORE (R-S.C.), who said it "doesn't look good" for the EPA head.

Sen. Susan Collins Susan Margaret CollinsGraham: GOP will confirm Trump's Supreme Court nominee before the election Gardner signals support for taking up Supreme Court nominee this year Tumultuous court battle upends fight for Senate MORE (R-Maine) also said Pruitt's fate in the administration is up to Trump.

"This daily drip of accusations, of excessive spending and ethical violations served to further distract the agency from accomplishing its very important mission," Collins told CNN's "State of the Union."