Josh Earnest, the White House press secretary, seemed to try to tamp down the Baratz tempest on Thursday, saying that it was “readily apparent that the apology was warranted,” but declining to comment further because, as he put it, Mr. Netanyahu’s staff appointments were “decisions that he will rightfully make on his own.”

A State Department spokesman described Mr. Baratz’s statements as “troublesome and hurtful” and said Mr. Kerry had spoken to Mr. Netanyahu about the matter.

Some Israeli analysts said Mr. Netanyahu’s selection of such an outspoken ideologue to shape his diplomatic message and serve as a major spokesman to the world reflected the prime minister’s blindness to Israel’s increasing isolation. If Mr. Baratz were confirmed, he would join a growing list of recent right-wing appointees — including a United Nations ambassador and deputy foreign minister who oppose the establishment of a Palestinian state — that have raised eyebrows in Washington and other Western capitals.

“He’s giving a very strong negative message to the world, which is, ‘I don’t care about public diplomacy, I have a right-wing government, I have a right-wing policy, and I’m going to send people who are offensive,’” said Mitchell Barak, a political consultant in Jerusalem. “Every time, people say, ‘Oh, he must have made a mistake, we can’t take it seriously,’ but frankly, he seems to be sending a very clear message, which is, ‘I’m going to appoint the hard-core ideologues, I’m not going to even pay lip service to any diplomatic solution, I’m going to entrench myself more.’”

Mr. Netanyahu also has been struggling of late with message discipline. Last week, he reprimanded the deputy foreign minister, Tzipi Hotovely, after she told an interviewer that she dreamed of raising the Israeli flag atop the Temple Mount, the Old City site known to Muslims as the Noble Sanctuary.

He also retracted his own statement that it was a Palestinian cleric, not Hitler, who came up with the idea to annihilate Europe’s Jews.

On Thursday, Israeli journalists had a field day parsing the Facebook profile and other public writings of Mr. Baratz, 42, who has a Ph.D. in philosophy and founded Mida, a right-wing website. Channel 2 news reported that even Mr. Baratz’s boss-to-be was not spared: “Netanyahu,” the nominee wrote in March, after the prime minister’s contentious speech in Congress against the nuclear deal with Iran, “perhaps by chance is beginning faintly to reflect the pale shadow of something that vaguely recalls Netanyahu of 1996.”