MOSCOW — Russian lawmakers, moving to further restrict freedom of speech, passed bills on Thursday that would introduce jail terms and fines for insulting the government online or spreading so-called fake news.

The bills are seen as an effort to pre-empt and control public criticism as Russia’s prolonged economic stagnation pushes down the Kremlin’s approval ratings. They reflect a nearly two-decade-long project by President Vladimir V. Putin to put information flow under state control, a push made more difficult by the growth of the internet.

The new measures await final passage in the upper chamber of parliament and Mr. Putin’s signature. He has expressed support for restrictions against insulting the state online.

One set of bills passed by the lower house, the Duma, would subject private individuals to fines of up to $3,000 or 15 days of administrative arrest for insulting the government online. Individuals would face fines of up to $6,000 for posting what is termed fake news.