Since mid-October, she had rarely been seen by reporters at the State Department as Palladino took the lead.
Donald Trump's appointment of Heather Nauert - the state department spokeswoman and a former Fox News anchor - as the new USA ambassador to the United Nations is widely being interpreted as bad news for the UN.
As a New York-based anchor and correspondent at the Fox News Channel, Nauert oversaw breaking news, anchored programs, covered global and domestic crises and interviewed senior elected and military officials.
"She's very talented, very smart, very quick, and I think she's going to be respected by all", Trump said.
"What we've really discovered over the last two years is that even when you have a relatively mainstream, relatively collegial, relatively influential ambassador to the United Nations like Haley, that only buys you a limited degree of protection from a president like Trump".
If confirmed by the Senate, the former Fox News anchor would replace Nikki Haley.
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They "seem to show a great deal of empathy towards some of the sad stories that I read with them", Mr Cox said. His daughter understood that her bullying was the reason she was forced to walk, Cox said.
"Nauert is a very good public operator, and should do a professional job presenting USA policy at the UN", Richard Gowan, a senior fellow at the United Nations University's Center for Policy Research, said in an email. Haley had lobbied hard to get the resolution passed, but couldn't garner the two-thirds majority needed.
But her inexperience sometimes shone through: in June she cited the D-day landings as evidence of the longstanding relationship between Washington and Berlin. Before joining the State Department, Nauert did not have any previous government or diplomatic experience.
The moves were expected; Trump's comments offered official confirmation.
The announcement comes hours after a resolution championed by Haley condemning the Hamas terror group failed to pass in the General Assembly.
United Nations diplomats say that behind the scenes negotiations are central to an ambassador's job, and that presentation skills are also important.
Ms Nauert worked for Fox News from 1998 to 2005 and, after two years away during which she worked for ABC, she returned to Fox in 2007, later becoming a presenter for Fox & Friends.
UN diplomats said privately they hoped that Nauert will be an advocate for the United Nations within the Trump administration, to counter the anti-UN views of national security adviser John Bolton.
Haley is a powerful presence in the administration and won Cabinet-level status despite officially reporting to Secretary of State Mike Pompeo.