USA intelligence officials accuse the Kremlin of using Russian media organisations it finances to influence US voters, and this week Washington required Russian state broadcaster RT to register a US -based affiliate company as a "foreign agent".
The law could require designated media outlets to disclose where they get their funding and how they spend it, though the bill does not specify on what basis foreign media would be compelled to register.
Once registered, they will face requirements now applied to foreign-funded non-governmental organisations.
The bill will pass to the upper house, which is expected to approve it, and then to Putin for signing in the next two weeks.
Its passing follows RT registering with the US Justice Department following claims from US intelligence agencies that the television channel served as a Kremlin tool to meddle in the 2016 presidential election.
Russian Federation has denied it interfered in last year's United States presidential election.
Russian President Vladimir Putin gives a news conference at his country residence of Novo-Ogaryova, outside Moscow, on March 4, 2014.
Russian Federation moves to label foreign media as 'foreign agents'
The State Duma has passed an amendment, which allows the state to recognize foreign media receiving financing from overseas as "foreign agents" in third and final reading.
Russian MPs backed amendments that would allow global media that receive financing from overseas to be classified as "foreign agents", RIA Novosti news agency reported, a measure previously used only against NGOs.
"I would like to hope that it will only be used once and there will be no need for more retaliatory action", he added.
After the registration, the news outlets would be subject to requirements that already apply to foreign-funded nongovernmental organization under a 2012 law on foreign agents.
Companies will be forced to declare their finances, funding and staffing if the rules are implemented. Critics of the law have said the definition of political activity is so loose that it could be used against nearly any nongovernmental organization.
Amnesty International said the bill was an attack on media freedom.
Military coup rumours in Zimbabwe after broadcaster seized
The United States on Wednesday encouraged its citizens residing here to "shelter in place" amid political turmoil in the country. Mugabe, who has held the presidency for more than two decades, remains the only leader many in the country have ever known.