WASHINGTON—Top Trump administration officials raced on Thursday to deny authorship of an anonymous opinion column critical of the president, and senior White House aides privately acknowledged they are unlikely to root out the person they view as an internal saboteur.

President Trump was watching closely, according to a person familiar with the matter, as the stream of denials poured in from senior officials and confidants, including Vice President Mike Pence, who sought to distance themselves from the New York Times column that described a secret resistance movement inside the administration aimed at curtailing Mr. Trump’s “worst inclinations.”

At a rally in Montana Thursday night, Mr. Trump criticized the Times for publishing the column and said it was likely a “low-level” staffer in the administration. “Virtually you know it’s treason,” he said.

An informal search for the author was being led in part by White House chief of staff John Kelly, but no formal investigation was under way inside the West Wing, a senior White House official said. The official said there were open questions about available legal remedies, and that the White House counsel’s office, which would otherwise lead a more formal probe, was consumed by the confirmation battle over Supreme Court nominee Brett Kavanaugh.

There were only rudimentary plans for a public pushback on the column, another White House official said. Aides were directed to refer reporters to a statement from White House press secretary Sarah Sanders that referred to the author as a “coward.”