Amid reports that President Trump is increasingly frustrated and angry in his job performance, the White House called in the Marines on Thursday in the form of chief of staff John F. Kelly, who chided the media for exaggerating dissension in the West Wing and said he’s not quitting his new post.

Mr. Kelly, a retired four-star Marine general, made a surprise appearance in the White House press briefing room to address the administration’s challenges head-on. He said he shares some of the president’s frustrations with the media.

“Although I read it all the time pretty consistently, I’m not quitting today,” Mr. Kelly told reporters tongue-in-cheek. “I just talked to the president, I don’t think I’m being fired today. I’m not so frustrated in this job that I’m thinking of leaving.”

The president brought in Mr. Kelly in late July from his job as Secretary of Homeland Security to replace Reince Priebus, who was ousted amid staff turmoil, turnover, legislative losses and a widely perceived lack of discipline in the West Wing. Since then, Mr. Kelly has moved to control the flow of information to the president, a traditional role of the chief of staff as gatekeeper.

“He’s one of the finest people I have ever had the privilege to know,” Mr. Trump said Thursday. “We are deeply fortunate that he is now here at the White House as our chief of staff.”

Mr. Kelly’s calm on-camera appearance came at a moment when the president is in the midst of numerous feuds, on social media or in person. In recent days he’s battled with Senate Foreign Relations Chairman Bob Corker, the Tennessee Republican who said Mr. Trump requires “adult day care;” with the mayor of hurricane-ravaged San Juan, Puerto Rico, who accused the president of “genocide” for the administration’s allegedly slow disaster response; with NBC News (Mr. Trump suggested the government revoke licensing over its “disgusting fake news;”) and with Secretary of State Rex W. Tillerson, who reportedly called Mr. Trump a “moron” and prompted a barb from the president that he would win an IQ test between the two.

Media reports, citing mostly anonymous sources, have portrayed Mr. Trump as ready to blow his stack and in the grip of dark moods as his legislative agenda has stalled and he endorsed the losing candidate in an Alabama Senate race. Vanity Fair quoted a presidential friend saying Mr. Trump has griped that he “hates everybody in the White House.”

Against that chaotic tableau, Mr. Kelly sought to present a picture of low-key order.

But Mr. Kelly acknowledged that Mr. Trump, whom he called “a man of action,” is often frustrated with Washington.

“The Congress has been frustrating to him,” Mr. Kelly said. “Of course, our government is designed to be slow, and it is. I would say his great frustration is the process that he now finds himself, because in his view the solutions are obvious.”

He said the attributes that attracted many voters to Mr. Trump — a Washington outsider who is a businessman — also lead to some of the president’s exasperation with the job.

“Whether it’s tax cuts and tax reform, health care, infrastructure programs, strengthening our military — to him, these all seems like obvious things that need to be done to protect the American people, bring jobs back,” Mr. Kelly said. “These are all the things that he sees as vital to protect the American people or to advance the American economy or what not. And the process is so slow and so hard sometimes to deal with.”

He said he shares some of Mr. Trump’s vexation about the media.

“It is astounding to me how much is misreported,” Mr. Kelly said, advising reporters to “develop some better sources.”

Asked about the president’s feud with Mr. Corker, whom Mr. Trump called foolish, the chief of staff said, “He’s a straightforward guy, the president is. When members of Congress say things that are unfair or critical, the president has a right to defend himself.”

While critics have called for someone in the White House to control Mr. Trump’s Twitter account, Mr. Kelly said that’s not his job.

“I was not brought to this job to control anything but the flow of information to our president, so that he can make the best decisions,” Mr. Kelly said. “He’s a decisive guy. He’s a very thoughtful man. I can guarantee to you that he is now presented with options — well thought-out options. Those options are discussed in detail with his team. And then he comes up with the right decision.”

“This is the most important job I’ve ever had,” Mr. Kelly said. “I’m not frustrated. This is really, really hard work running the United States of America. There [were] an awful lot of things that, in my view, were kicked down the road that have come home to roost pretty much right now, that have to be dealt with.”

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