“Americans should exercise caution before accepting as true any stories attributed to anonymous ‘officials,’ particularly when they do not identify the country — let alone the branch or agency of government — with which the alleged sources supposedly are affiliated,” Mr. Rosenstein said in the statement.

He did not cite specific reports. The Justice Department released Mr. Rosenstein’s statement after 9 p.m., a few hours after The Washington Post reported that the special counsel was investigating the business dealings of Jared Kushner, Mr. Trump’s son-in-law and adviser. That report was attributed to unnamed American officials.

Asked about the impetus for the statement, a Justice Department spokesman declined to comment. Mr. Rosenstein did not respond to an email seeking comment on Thursday night.