A general strike against tough austerity measures is under way in Greece, with trade unions calling for "mass mobilisation" of protesters.
The 24-hour action caused some disruption to public transport and reduced staffing at hospitals.
Organisers are demanding an end to spending cuts and tax rises, which the government says are needed to lead Greece out of six years of recession.
But a BBC reporter says the protests so far have been the smallest for months.
The cabinet of Prime Minister Antonis Samaras says the policies are part of continuing moves to ensure more bailout money from international creditors.
The 24-hour strike officially began at midnight. Trains and ferries were brought to a standstill, and other public transport was disrupted.
However, many shops stayed open as the Labour Day public holiday was moved to next Tuesday - after Greek Orthodox Easter.
In Athens, hundreds of people rallied outside parliament in Syntagma Square, waving flags and banners.
Pensioner Antonis Mosiadis said politicians should listen to the people.
"The fight continues and it will continue. They have gone deaf over there [in parliament] and if we do not continue this fight, soon they will destroy us," he said.
The BBC's Mark Lowen in Athens says there have been far fewer strikes and protests this year, and there is a feeling the civil unrest is beginning to die down.
Nevertheless, demonstrations are planned across the country, with police on alert for a repeat of past violence.
The two largest unions - the GSEE and ADEDY - have said that the action will focus on demands to end austerity.
They say that government measures have led to the country's record unemployment rate of 27%, including almost 60% among young people.
"Our message today is very clear: Enough with these policies which hurt people and make the poor poorer," Ilias Iliopoulos, general secretary of ADEDY, told Reuters news agency.
"The government must take back the austerity measures, people can't take it any more."
Mr Samaras has defended his policies, insisting that this year of recession will be the country's last.
Nearly 3bn euros (£2.5bn; $4bn) of bailout money were approved this week, with another 6bn euros set to come on 13 May.
Since 2010, the European Union and the IMF have promised more than 200bn euros in lending for Greece. Talk of exit from the eurozone has receded.
However, our correspondent says the optimism has not reached the streets, where the mood remains dire given the record unemployment levels.
Other May Day action has been taking place across in the world:
- In central Moscow, at least 70,000 people turned out for a trade union parade backed by the governing United Russia Party, according to police figures
- In Istanbul, police used tear gas and water cannon after protesters defied a ban on May Day demonstrations; officials say the ban is to protect renovation work taking place at Taksim Square, a traditional rallying point
- Protesters angered by the deaths of hundreds in a recent building collapse in Bangladesh marched through the capital, Dhaka
- Rallies were called in more than 80 cities in Spain
- Thousands of Filipinos marched in Manila demanding the government protect jobs and improve worker contracts
- Cambodian workers rallied in Phnom Penh, calling for higher wages
- Some 55,000 marched in Indonesia's capital, Jakarta, protesting against low wages and outsourcing
- Trade unions held demonstrations in Tokyo, with calls for more youth employment one of the main focuses
- In Hong Kong, trade unions said they were expecting 5,000 people to march in support of striking dock workers.