Russia’s Parliament approved legislation on Wednesday that could require foreign media organizations operating in Russia to label news they produce the work of a “foreign agent,” the latest step in the unraveling of relations since the United States accused Russia of meddling in the 2016 presidential election.

The measure will become law if passed by the Russian Senate and signed by President Vladimir V. Putin. Over the weekend, however, Mr. Putin expressed some doubts, saying the rule may go too far.

The proposed new regulation is evidently intended as retaliation for reporting requirements imposed by the Department of Justice on the American affiliate of RT, the Russian state-run TV news outlet that American intelligence agencies say is a propaganda tool of the Kremlin.

Last week, acting in accordance with the Foreign Agents Registration Act, a 1938 law that was aimed at Nazi propaganda organs, the Justice Department required RT to identify itself as a “foreign agent.” Under that law, foreign agents are required to file reports on the sources of their funding and on all activities intended to influence a lawmaker or other government representative. It is not clear what that would mean for RT’s reporters.