The State Duma bill, which passed 346 - 17 at its first of three readings, says any person who receives financial or any other kind of support from abroad can be designated a foreign agent.
The bill also introduces a new category of "persons affiliated with a foreign agent." Co-author Andrei Lugovoy said this could include relatives of foreign agents or others who helped them carry out their activities.
Under the bill, Russia’s media watchdog Roskomnadzor will have the right to block foreign agents’ websites at the request of the Ministry of Justice without a court decision.
Lugovoy accused various unnamed Russian public figures of having received "special training" in the United Kingdon, which he accused of seeking to destroy Russia from within.
Foreign agents are required by law to label any publications, including on social media, with a lengthy disclaimer, regularly report on their income and spending, and undergo financial audits.
"Naturally, those organizations that engage in Russia's internal affairs for foreign money must be under the most severe control. Period. We have hundreds, if not thousands of materials on such organisations," said Adalbi Shkhagoshev, a deputy from Vladimir Putin's dominant United Russia party.
The tightening of the "foreign agents" law comes nearly 15 weeks into Russia's war in Ukraine. President Putin said in March that the West was trying to use a "fifth column" to undermine the country and declared that Russians "will always be able to distinguish the true patriots from the scum and the traitors".
Russia’s first law on foreign agents was adopted in 2012. It has since been expanded to include non-profit organizations, media outlets and individual Russian citizens including journalists and activists.
At present, the list includes 166 individuals and legal entities. The designation has been used to target media outlets including the Voice of America, German broadcaster Deutsche Welle, independent news site Mediazona and the Dozhd TV channel.