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When President Trump said on Twitter that an Uzbek man charged with using a pickup truck to kill eight people “SHOULD GET DEATH PENALTY,” the man’s lawyers asked a judge to bar prosecutors from seeking execution, saying the decision had become too politicized.

But a federal judge in Manhattan ruled on Thursday that prosecutors could seek capital punishment despite the president’s comments.

Defense lawyers had argued the president’s tweet and other statements he made on Twitter had put political pressure on the attorney general at the time, Jeff Sessions, to seek a death sentence. The lawyers pointed to public reports that Mr. Trump was considering firing the attorney general for not following his wishes, and said Mr. Sessions would not be able to make an impartial decision.