The Confederation of German Trade Unions (DGB) condemned xenophobia and right-wing extremism at its traditional Labour Day rally on Sunday in the south-western city of Stuttgart, as violent incidents were reported across the country.
"The demands of right-wing extremists have nothing to do with social cohesion, social justice, fair globalization or solidarity," DGB leader Reiner Hoffmann said, referring to the congress of the populist Alternative for Germany (AfD) party also taking place in the city over the weekend.
In particular, he criticized the party's anti-refugee propaganda.
The DGB rally also addressed the abuse of temporary work contracts by employers.
Some 390,000 people attended more than 500 trade union events across the country, according to the DGB.
Following a DGB rally in the northern city of Hamburg, around 100 protesters attacked police, pelting officers with stones and bottles. Police used water cannon to contain the crowds.
Thousands of revellers and protesters gathered in Berlin's traditionally left-wing Kreuzberg district for the annual street party and for the Revolutionary May 1 Demonstration. Organizers said 20,000 people had taken part, while police put the figure at 13,000.
Following the demonstration, black-clad demonstrators attacked police, throwing stones and bottles. Police made multiple arrests and several people were injured, including three police officers.
The Berlin district has become known for May Day violence in recent years, but police described this year's scene as largely positive.
In the northeastern city of Schwerin police sent off around 100 masked leftist protesters, as 400 followers of the right-wing nationalist NPD party were marching nearby.
Clashes were also reported from an NPD rally in the western German city of Bochum, where NPD opponents injured two police as they were throwing stones.
Right-wing protesters jeered and whistled at Justice Minister Heiko Maas as he addressed a crowd in the eastern city of Zwickau, where police had to guard the podium.
In the eastern city of Plauen several people were injured as right-wing and left-wing protesters clashed with police. Security forces called the incident a "massive outbreak of violence" as neo-Nazis from all over Germany had gathered in the city.
Police in the western German city of Dortmund meanwhile arrested two suspects in connection with attacks on visitors at the Mayday Techo Party, where some 20,000 people raved through the night.
According to police, five or six members of a gang had attacked partygoers using tear gas and stolen their necklaces. Three police were lightly injured during the arrests.
In neighbouring France there were also isolated clashes between police and demonstrators on the sidelines of marches by unions against labour reforms being considered by parliament.
In Paris, there were clashes at the Place de la Republique. Nationwide, some 18 people were arrested, the Interior Ministry said.