Kelly's extraordinary statements are the latest examples of Trump administration officials professing their loyalty publicly Trump, refuting reports that suggest problems in the chaotic administration.
Nielsen had been chief of staff to John Kelly when he was Trump's first homeland security secretary.
'I would just offer to you that although I read it all the time pretty consistently, I'm not quitting today, ' he said during a surprise appearance at a White House news conference. "I don't think I'm being fired today, and I'm not so frustrated in this job that I'm thinking of leaving".
"Unless things change, I'm not quitting, I'm not getting fired and I don't think I'll fire anyone tomorrow", the former secretary of homeland security told reporters, drawing some laughter.
Kelly took issue with the notion that he is a "failure" for not controlling Trump's frequent tweeting, which has not stopped during his tenure as chief of staff.
Ophelia is 10th straight storm to reach hurricane
National Hurricane Center said the storm was located Thursday about 715 miles (1,145 kilometers) southwest of the Azores. This could bring a blast of high winds to the Emerald Isle, particularly the western half of Ireland early next week.
There have been recent rumors and reports about the retired four-starMarine Corps general and the challenges of being Trump's chief of staff. "She is ready on Day One", Trump said.
Nielsen, however, has drawn some resentment in her current White House position, as she and Kelly have tried to instil more discipline at the White House. "Some person that works way down inside an office, well, develop some better sources".
When asked what frustrates the president, Kelly laughed and said he thought that it was the media.
"A state that has developed a pretty good ICBM (missile) capability and is developing a pretty good nuclear re-entry vehicle, I would believe ... that that state simply can not have the ability to reach the homeland", Kelly said. "I look forward to working closely with the Administration and Ranking Member McCaskill to expedite the consideration of Ms. Nielsen's nomination and help make America safer and more secure".