Donald Trump’s chief of staff has made an extraordinary public appearance to deny that he is about to resign or be fired.

John Kelly, who has so far maintained a low public profile at the White House, on Thursday described the president as a “thoughtful” and “straightforward guy” and joined his criticism of the media over what he claimed are false reports.

“Although I read it all the time pretty consistently, I’m not quitting today,” Kelly, 67, said from the lectern in the White House briefing room, a position normally occupied by press secretary Sarah Sanders. “I don’t believe – and I just talked to the president – I don’t think I’m being fired today. And I’m not so frustrated in this job that I’m thinking of leaving. I will tell you this is the hardest job I’ve ever had, this is in my view the most important job I’ve had.

“I’m not quitting, I’m not getting fired, and I don’t think they’ll fire anyone tomorrow.”

The retired marine corps general and former secretary of homeland security was appointed nine weeks ago to impose new discipline in the West Wing. But two viral images have fuelled speculation around discontent. One showed him staring at the floor at a press conference in New York as Trump rambled about “both sides” being to blame for violence at a white supremacist march in Charlottesville, Virginia. Another caught Kelly with his head in his hands during the president’s address to the UN general assembly.

John Kelly, Jared Kushner and Donald Trump at a meeting with Spain’s prime minister on 26 September 26 2017. Photograph: Jonathan Ernst/Reuters

But on Thursday he was in a humorous mood and said: “You guys with the cameras always catch me when I’m thinking hard, and it looks like I’m frustrated and mad.”

There have been reports that Kelly is unhappy in the job as Trump’s legislative agenda stalls and the president continues to picks fights with everyone from senators to NFL players to a mayor in hurricate-hit Puerto Rico.

Kelly blamed the media for misleading stories about discord at the White House, albeit in more polite language than the president customarily uses. He said: “This is hard, hard work and my only frustration, with all due respect to everyone in the room, is when I come to work in the morning and read about things I allegedly said, or things Mr Trump allegedly said, or people who are going to be fired or whatever, and it’s just not true.”

And asked about the president’s own frustrations, Kelly replied frankly: “One of his frustrations is you. All of you. Not all of you, but many of you... It is astounding to me how much is misreported. I will give you the benefit of the doubt that you are operating off of contacts, leaks, whatever you call them, but I will just offer to you the advice, I’d say maybe develop some better sources.”

Congress has also been frustrating to the president, Kelly added. “His sense as a man who is outside the Washington arena, a businessman, much more of a man of action, I would say his great frustration is the process he now finds himself [in] because, in his view, the solutions are obvious.”

The chief of staff also said the North Korean nuclear and missile threat is “manageable” for now but the isolated nation cannot be allowed to develop the ability to strike the US homeland. Kelly said Americans should be “concerned” about North Korea since it has developed an intercontinental ballistic missile capability and is developing a vehicle that would allow a missile to survive re-entry into the earth’s atmosphere.

Although Trump recently declared that secretary of state Rex Tillerson was “wasting his time” trying to negotiate Pyongyang, Kelly added: “Let’s hope diplomacy works.”

Kelly also said of Trump: “I hear him most say about nuclear weapons that, ‘Wouldn’t it be great if we could get rid of them all?’ as opposed to ‘We need 10 times more’.”

Kelly’s insistence that he is remaining in post comes after a turbulent nine months that have witnessed the departures of his predecessor Reince Priebus, press secretary Sean Spicer, national security adviser Michael Flynn, health secretary Tom Price and others.

Later on Thursday, announcing his nomination of Kirstjen Nielsen for homeland security secretary in the east room, Trump lavished praise on Kelly and asked him to stand. The chief of staff did so with a smile and a salute.