The move is retaliation for the withdrawal of a Russian state-funded television station's credentials in the US.
The State Duma's procedural committee proposed that the house vote on the measure Wednesday. The upper house, the Federation Council, plans to take similar action later this month.
In the US, a committee governing Capitol Hill access for broadcast journalists withdrew credentials for Russia's state-funded RT television after it complied with a US demand that it register as a foreign agent.
US intelligence agencies have alleged that RT served as a tool for the Kremlin to meddle in the 2016 US presidential election. Moscow has denied any interference.
The law leaves it to the Russian Justice Ministry to single them out.
Foreign correspondents in Russia can currently access the parliament and some government agencies using press credentials issued by the Foreign Ministry.