WASHINGTON — Rod J. Rosenstein, the deputy attorney general, encouraged Americans in a statement issued late Thursday to be “skeptical about anonymous allegations” after a string of recent news reports about the evolving focus of the special counsel’s investigation into Russia’s election interference and possible collusion with President Trump’s associates.

“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.