President Vladimir Putin has criticised Russia's government and its regional authorities over controversial changes to the social security system.
Most participants in the protests are urban pensioners
Mr Putin said the implementation had not been thought through, and had left some people worse off.
He ordered a pension rise of at least $6 a month, but said the reforms to the old benefits system were needed.
There have been calls for the cabinet to resign following protests against the scrapping of social benefits.
Mr Putin said: "The government and the regions have not completely carried out their task that we spoke of - which was to not make the situation of those who depend on state assistance any worse."
The authorities seem to be backing down on the reform that envisaged a total revamp of the Soviet-era welfare system.
In many Russian regions a compromise has been reached on transport costs for pensioners, policemen and the military.
The wave of protests against new laws replacing non-monetary benefits, such as free transport for some categories of the population, have continued for more than a week.
On Monday, pensioners blocked traffic on key highways in European Russia and the Far East.
This followed protests on Sunday when 10,000 pensioners were joined on a march by young left-wing activists in St Petersburg.
An 80-year-old man died when protesters attacked an expensive car and its owner reversed to get away from the crowd.
In many regions, including St Petersburg and around Moscow, the authorities have agreed a compromise on the transport issue by either restoring free transport for pensioners or reducing fares.
But more protests are expected at the end of the month, when pensioners will receive bills for electricity and other utilities, which the state has decided not to subsidise any longer.
The Fatherland and the Communist Party control minority factions in the lower chamber of the Russian parliament, the Duma.
They do not have enough support to push the no-confidence move through the chamber, which is firmly controlled by the pro-presidential United Russia party.
But a senior member of United Russia, vice-speaker Lyubov Sliska, said on Monday that "voluntary resignations of some ministers could considerably ease tensions".