Senior lawmaker Alexander Khinshtein said Friday that draft legislation forcing major foreign IT companies to establish Russian offices had been submitted to parliament.
"It concerns IT companies whose daily audience in Russia tops 500,000 people," Khinshtein, the head of the information policy, IT and communications committee at parliament's lower house State Duma, wrote on his Telegram channel.
"We expect that market players will treat this new measure with understanding."
If foreign technology companies refuse to comply, they will face penalties including a ban on advertising their services, a ban on collecting payments, or partial or full blockage in the country, Khinshtein said.
Another lawmaker, Anton Gorelkin, said he expected the legislation would make tech giants more attentive to Russian demands.
"With the appearance of necessary legislation cooperation should get better," Gorelkin, a member of the information policy committee at the State Duma, wrote on Telegram.
In January, Russian authorities accused foreign social media platforms of interfering in the country's domestic affairs by not deleting calls to protest in support of jailed opposition leader Alexei Navalny.
The state telecommunications watchdog in March imposed slowdowns on Twitter's services, accusing it of failing to remove content related to child pornography, drug use and calls for minors to commit suicide.
Twitter said at the time it was "deeply concerned by increased attempts to block and throttle online public conversation".