The deputy’s job was denied for Elliott Abrams, a conservative who had served under President Ronald Reagan and President George W. Bush, deals a blow to Mr. Tillerson in his first week on the job. The rejection of Mr. Abrams leaves Mr. Tillerson without a sherpa to help guide the first-time government official around the State Department headquarters.

Mr. Trump had a productive meeting with Mr. Abrams on Tuesday, according to a White House official and a person close to Mr. Abrams. But after it took place, Mr. Trump learned of Mr. Abrams’s pointed criticisms of the president when he was running for president, the administration official said. Among those criticisms was a column headlined “When You Can’t Stand Your Candidate,” which appeared in May 2016 in The Weekly Standard.

Mr. Trump has been increasingly focused on who was with him or against him during his campaign, according to several people who have spoken with him in recent days.

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.

Democrats turn up heat on Flynn

The revelation that Michael T. Flynn, President Trump’s national security adviser, apparently discussed sanctions with Russia’s ambassador to the United States in the weeks before the inauguration has given Democrats a new cudgel to revive discussions of Mr. Trump’s ties to Russian President Vladimir V. Putin.