The ruling United Russia party held the largest rally in central Moscow along with a trade union organization, which demanded pensions be raised to at least 40% from the current 5-15% of earlier salaries by 2008, a rise in minimal salaries to the subsistence level and other measures to curb poverty. Police said 20,000 people participated.
The Communist Party and its allies, which included outlawed radical National Bolshevik Party members, marched down to Teatralnaya square in central Moscow, where a bust to Karl Marx is located, chanting "For free elections" and "For independence."
Communist leader Gennady Zyuganov, who is back from his trip to Latin America and conveyed regards to participants from Cuba's Fidel Castro and Venezuelan President Hugo Chavez, said some 50,000 people had gathered on the square. Police put the figure much lower.
Police mounted a large presence near the square, and participants had to walk through metal detectors to join the rally.
A total of 12 gatherings were held in the capital Tuesday involving members and supporters of 14 parties, police said adding their number reached 45,000.
No incidents have been reported in Moscow and St. Petersburg, where opposition groups, including Yabloko and United Civil Front, also held demonstrations in the wake of a harsh police crackdown on their march in late April.
Official reports said 250 and 170 people were arrested in both cities during the unsanctioned rallies, which demanded the president's resignation.
Marches were also organized across Russia, including its troubled Caucasus republic of Chechnya, where demonstrations took place for the first time in 16 years.
In Soviet times, May Day holiday, glorifying workers, was celebrated by pompous parades on Red .Square After the collapse of the Soviet Union in 1991, the Communists used the holiday to stage anti-government protests. But this year, the three-day holidays are regarded by many as