Demonstrations were conducted in at least three other cities in the Moscow region, in the capital of Tatarstan and, for the fourth consecutive day, in Samara in central Russia. In St. Petersburg, several thousand demonstrators blocked the city's main boulevard, with some calling for President Vladimir Putin's resignation.
Taken together, the protests are the largest and most passionate since Putin came to power in 2000.
They appear to have tapped into discontent with Putin's government and the party that dominates the Russian legislature, United Russia.
''It is spontaneous, and this is the most dangerous thing for the authorities,'' said Mikhail Yermakov, 67, a retired engineer.
The law, which took effect on Jan. 1, replaced benefits like free public transportation and subsidies for housing, prescriptions, telephones and other basic services with monthly cash payments starting at a little more than $7.
Some of those eligible have yet to receive any payments.
Putin and United Russia's leaders have defended the law as an important reform, ending a vestige of the old Soviet Communist system, but they clearly failed to anticipate the depth of opposition from those who relied most on the subsidies: millions of Russians living on pensions of less than $100 a month.
The protesters have denounced the new payments as insufficient to cover the cost of the benefits and as miserly for a country that recently reported a budget surplus of nearly $25 billion.
At a minimum, the protests have raised doubts about Putin's other proposed reforms, including those in banking, housing and electricity, which were supposed to be the centerpieces of his second term.
Protests have erupted in at least a dozen other cities, drawing thousands. In Tula, 110 miles south of Moscow, aging protesters clashed with bus conductors who refused to allow them to board city transport without paying.
The protests have included something still rare in today's Russia: personal criticism of Putin, who has remained popular by projecting an image of stability, one carefully protected by officials and state television.
The benefits law has already been credited, at least in part, with a slip in Putin's ratings, as well as a general decline in the public's mood.
