Haley addressed the comments in an interview with broadcaster CBS on Sunday.
"To undermine a president is really a dangerous thing and it is against the constitution and against what the Americans want," Haley told CBS.
Kelly said if providing the president "with the best and most open, legal and ethical staffing advice from across the [government] so he could make an informed decision is ‘working against Trump,’ then guilty as charged," in a response to The Washington Post.
The Trump White House has seen an unusually high number of sackings and resignations.
Tillerson was fired in March 2018, while Kelly left at the end the same year.
Some former White House staffers have painted a picture of chaos in the government in insider reports and revelatory books.
It was Haley's choice to end her posting at the United Nations in New York at the end of 2018. Rumours swirled about her political ambitions, with many speculating she had an eye on a future presidential run.
Trump tweeted Haley "good luck" on Sunday ahead of the book release.
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