Nielsen was former DHS Secretary John Kelly's deputy when he served in that role and moved with Kelly to the White House when he was tapped to be Trump's chief of staff.
"It's amusing, I read in the paper-you all know, you write it-that I have been a failure at controlling the president or a failure at controlling his tweeting and all that", Kelly said.
Asked by a reporter if he was frustrated at all, Kelly said, "No, I'm not frustrated".
Kelly took over as President Trump's Chief of Staff on July 28, bringing a new sense of order to the West Wing.
Kelly blamed the media for misleading stories about discord at the White House, albeit in more polite language than the president customarily uses. Another caught Kelly with his head in his hands during the president's address to the United Nations general assembly. "She is ready on Day One", Trump said.
But even before Trump formally announced Nielsen's appointment during an East Room ceremony that was attended by much of the Cabinet and senior members of the White House staff, the top Democrat on a key committee signalled that he had questions about Nielsen's background.
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"Some person that works way down inside an office or - Well, just develop some better sources", he said. "But I would just offer to you the advice", he added.
Prior to joining Kelly at Homeland Security, Nielsen was president of the firm Sunesis Consulting. People close to her "have counseled her to lighten up and to pay more attention to the perfunctory niceties of a not-so-nice-job", they wrote when she became deputy White House chief of staff.
"Right now we think the threat is manageable, but over time, if it grows beyond where it is today, let's hope that diplomacy works", Kelly said.
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.
In a statement, Senator Ron Johnson said, "Ms. Nielsen's long history of service with the Department, her cybersecurity experience and her tenure serving with General John Kelly would serve her well as the next Secretary of the Department of Homeland Security". The chief of staff did so with a smile and a salute.