MOSCOW (Reuters) - The Russian lower house of parliament, the State Duma, has approved a proposal to launch an investigation into U.S. media organisations that operate in Russia, it said in a statement posted on its web site late on Friday.

The investigation, which will be conducted by the Duma's information policy, technologies and communications committee, will check whether CNN, the Voice of America, Radio Liberty and "other American media" are complying with Russian law.

The statement said the Duma backed the move on Friday evening after Konstantin Zatulin, an MP from the pro-Kremlin United Russia party, proposed an investigation to retaliate for what he called a "repressive" U.S. move against Russian state-funded broadcaster RT.

He said he was referring to an initiative by U.S. Senator Jeanne Shaheen, who has introduced a bill to empower the Justice Department to investigate possible violations of the Foreign Agents Registration Act by RT.

Shaheen, a Democrat, cited a U.S. intelligence agency assessment that suggested RT was part of a Russian influence campaign to help Donald Trump win the White House last year. The Kremlin and RT have strongly rejected that allegation.

Foreign media in Russia are overseen by the Russian Foreign Ministry, whose spokeswoman Maria Zakharova this week singled out Shaheen's demarche for criticism, quipping ironically that the senator should have included a clause drawing up a list of books for burning.

The U.S. move also solicited the ire of Margarita Simonyan, RT's editor-in-chief, who on Wednesday told the daily Izvestia it had echoes of the activities of U.S. Senator Joseph McCarthy, who oversaw a campaign to expose people he regarded as communists in the 1950s.

(Reporting by Andrew Osborn; Editing by Julia Glover)