The president’s abrupt reversal could anger those supporters if they view the decision as evidence that Mr. Trump exhibited weakness by caving to pressure from within his own administration.

In his tweets, Mr. Trump said that Justice Department officials had agreed to release the unredacted documents, but had also warned of what the president called “a perceived negative impact on the Russia probe.” The tweet did not explain further.

The president also said in the tweet — without elaboration — that “key Allies” had called to urge him not to declassify the documents.

According to a former American official and a former British official, the British government expressed grave concerns to the United States government about the release of classified information. The material includes direct references to conversations between American law enforcement officials and Christopher Steele, the former British spy who compiled a dossier alleging ties between the Trump campaign and Russia.

Britain’s objection, these former officials said, was over revealing Mr. Steele’s identity in an official document, regardless of whether he had been named in press reports.

Some of the documents at issue involve the beginnings of the Russia investigation, when law enforcement officials submitted an application seeking permission from the secretive Foreign Intelligence Surveillance Court to wiretap Mr. Page. Mr. Trump and his Republican allies have claimed that law enforcement officials misled the court to get that permission.

The president’s declassification order on Monday called on law enforcement officials to release about two dozen pages from the surveillance application. Much of the application has already been released, but Mr. Trump’s order would make more of the application available to the public.