Behind the scenes, Ms. Haley has pushed back against the nationalists in the Trump camp by lobbying for relatively higher ceilings for refugee resettlement. She has publicly praised Mr. Trump’s decision to abandon the climate agreement, but she has also acknowledged the fact of climate change.

She has said little, publicly, about the president’s handling of the white supremacy rally in Charlottesville, Va., saying on Twitter only that she knows “the pain hate can cause.” But she issued a far more forthright letter to her staff. “Those who march spewing hate are few, but loud,” she wrote. “We must denounce them at every turn, and make them feel like they are on an island and isolate them the same way they wish to isolate others.”

Later, she said in a television interview that she had had “a private conversation” with the president about it.

Her office did not respond to numerous requests for an interview. She is a frequent guest on Sunday morning network television shows, though, and she favors news conferences at the White House, rather than at the United Nations.

She plays to Republican concerns about the United Nations by referring, frequently, to the need to cut “fat” from its budget. She is often the first in the administration to speak out on what she recognizes as the most high-profile foreign policy issues for her Republican base: including Israel and Iran, even if it means glossing over facts.

On Friday, for instance, she asserted that the latest sanctions stop North Korea from earning money by exporting its workers; the sanctions, in fact, stop countries from increasing how many North Korean laborers they can bring in.

In the case of Iran, she said in a speech at the American Enterprise Institute, a conservative research group, that Mr. Trump would be entirely justified if he decided to decertify the nuclear accord, even though the International Atomic Energy Agency has said Iran is complying with its obligations under the deal.