The law would complement another piece of legislation that forces non-government organizations that engage in "political activities" and receive money from abroad to register themselves using the same term, which is steeped in Cold-War era hostility.
"Media will be considered as such if they receive money or property greater than 50 percent of revenues from foreign governments and their organs, international and foreign organizations as well as foreign citizens and people without citizenship," Interfax reported.
It was not clear how widely the new rules would be applied, and whether they would apply to Russian media with foreign funding or all foreign media organizations. Russian officials were not immediately available for comment.
While the law would not hamper the activities of media, it is likely aimed at legitimizing those reliant on foreign funds and advertisers, and would consolidate the predominance of Kremlin-friendly state-owned media.
The Kremlin, which denies orchestrating a clampdown on dissent, has said the law is needed to tighten control over foreign-funded organizations operating in Russia to prevent them gathering intelligence for other governments.
Following the biggest protests against his nearly 13-year long rule, President Vladimir Putin has accused foreign governments, including the United States, of meddling in domestic politics.
Critics say the law aims to link those who have spoken out against Putin with foreign powers, who he has said wish to spark a Russian 'color revolution' like those that swept away Soviet-era leaders from Georgia and Ukraine in the early 2000s.
This year Russia closed the office of the US Agency for International Development, saying that the organization had tried to influence Russian politics - likely a reference to vote monitoring group Golos, which shed light on numerous vote fraud allegations in last year's parliamentary election.
Putin's top human rights adviser Mikhail Fedotov said the media law threatened to isolate Russia.
"These deputies are advocating an iron curtain," Interfax reported Fedotov as saying.
However, despite his title, Fedotov has relatively little influence over the president's decision-making.
MOSCOW (Reuters) -- Russian lawmakers introduced a bill to the state Duma, or lower house of parliament, on Friday which would force foreign-funded media to register as 'foreign agents', adding to a raft of bills that critics say is aimed at cracking down on dissent.