A renewed push then began for Ms. Craft, with advocates telling the president that she would have a smooth confirmation since she was recently confirmed by the Senate for her post in Canada. She also has some prior experience at the United Nations, having served as an alternate delegate to the world organization under the administration of President George W. Bush.

Mike Pompeo, the secretary of state, said in a statement that “Ambassador Craft has been an outstanding advocate for America’s national security and economic interests in Canada and she is extremely well qualified to do the same at the United Nations.”

John R. Bolton, the national security adviser and a former United Nations ambassador himself, backed the choice of Ms. Craft, according to a person familiar with the process.

After Ms. Nauert removed herself from the running, many Trump allies and former officials who represent Mr. Trump’s base made a public push for Richard Grenell, the ambassador to Germany, to get the nod. Those voices included Corey Lewandowski, Mr. Trump’s former campaign manager, and Sean Spicer, the former White House press secretary. Mr. Grenell was at the White House this week for meetings with senior administration officials, according to an administration official. But Mr. Trump had expressed hesitation about removing him from his post in Germany.

The United Nations ambassador position is not expected to remain a cabinet-level post, as it was under Ms. Haley.

Nonetheless, the post of ambassador to the United Nations is one of the most high-profile diplomatic positions in any White House administration, and in some ways the person holding the post is America’s face to the world.

As ambassador to Canada since the end of 2017, Ms. Craft served in the role during one of the most acrimonious periods in relations between Canada and the United States — a period buffeted by tortuous trade negotiations and rhetorical skirmishes during which President Trump referred to Prime Minister Justin Trudeau as “very dishonest and weak” and accused him of making up “false statements.”