Mr. Tillerson had argued strongly for Mr. Abrams. So had Jared Kushner, Mr. Trump’s son-in-law and a senior adviser. Senator Tom Cotton, Republican of Arkansas who is closely aligned with friends of Mr. Abrams’, and some members of the pro-Israel lobbying group Aipac, had been reaching out to Democratic senators to impress upon them the importance of Mr. Abrams receiving Senate confirmation.

Aides to Mr. Trump did not respond to an email seeking comment.