MOSCOW — President Vladimir V. Putin signed into law on Friday a measure that will impose heavy fines on people who organize or take part in unsanctioned demonstrations, giving the Russian authorities powerful leverage to clamp down on the large antigovernment street protests that began six months ago and seemed to be re-energized after Mr. Putin’s inauguration last month.

The law multiplies existing financial penalties for those who take part in a demonstration that harms people or property by a factor of more than 120, with potential fines of more than $9,000 for individuals, more than $18,000 for organizers and more than $30,000 for groups or companies. The penalties could also apply to people who participate in an approved demonstration but who violate the terms of their permit for the event.

Such penalties would be crushing for most Russians, given the average yearly salary of about $8,500, but the implications of the new law extend far beyond practical considerations. By all accounts, Mr. Putin flexed substantial political muscle to have the law adopted, brushing aside any concerns about being seen as restricting free speech or assembly and ignoring reservations even among some of his allies and supporters.

Although Mr. Putin has distanced himself from United Russia, the party that endorsed him for president, party leaders nonetheless used their slim majority in the State Duma, the lower house of Parliament, to overcome a remarkable filibuster by opposition lawmakers and approve the law late Tuesday night. It was approved by the upper chamber, the Federation Council, the next day with only one vote in opposition.