Tulsi Gabbard, the director of national intelligence, opted not to name a critic of Israel’s war in Gaza to a top post managing briefings for the president, after the proposed appointment upset some members of President Trump’s coalition, according to officials familiar with the deliberations.

Daniel Davis, a senior fellow at a Washington think tank who is skeptical of American intervention overseas, was undergoing a background check to become the deputy director for mission integration, the officials said. The post is a powerful job that oversees the compiling of the President’s Daily Brief, a compendium of intelligence assessments that goes to the White House and top policymakers.

But news of the proposed appointment generated blowback on the right. A senior administration official said Ms. Gabbard reconsidered her choice given the criticism, and other officials confirmed the decision.