Greece's two largest umbrella unions representing public- and private-sector workers, gathered for an anti-austerity rally in Athens and a march to Parliament, ekathimerini.com reported.
The Communist party and its union offshoot, meanwhile, met at a steel plant in Elefsina, where workers have been on strike for more than six months, prompting the closure of the Athens-Corinth national highway.
Seamen also called a strike that meant ferries were docked at the port of Piraeus until Wednesday.
In Athens, transit workers engaged in a three-hour work stoppage.
In Moscow, outgoing President Dmitry Medvedev and successor Vladimir Putin visited a popular bar after the May Day demonstration, ITAR-Tass reported. The spread included traditional dried fish, chips, nuts, pies, crayfish and beer.
Leaders of several trade unions, umbrella labor organizations, political parties and lawmakers also visited the pub after the demonstrations.
Demonstrators at the Holiday of Spring and Labor rally marched through along Moscow's main shopping street to Manezh Square, RIA Novosti reported. Participants chanted slogans calling for better protection of workers' rights and criticizing government plans to change the pension system.
The rally also targeted Russia's opposition movement, which called off its demonstration Tuesday to prepare for a March of Millions protest in Moscow Sunday.
Arrests were made in Moscow and St. Petersburg, where police detained 17 gay-rights activists at an opposition rally, the group Coming Out said.
Meanwhile, farmers association Coldiretti said nearly half of Italians used May Day for a picnic, not a rally, ANSA reported.
The organization said about 15 percent of Italians would stay at home.
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