Police deployed extra police in Berlin as three rallies were organized in the capital on Saturday. The day before, in her weekly video message, Chancellor Angela Merkel had defended German media and press freedom.
Berlin's authorities deployed 1,700 police on Saturday to keep watch over three parallel protests.
Berlin's Senator for the Interior Frank Henkel said it was the police's task to protect the constitutional right to assembly and "not the content of gatherings."
A "Nazi-free" march drew 4,500 participants, who walked from central Berlin's Hackeschen Markt plaza toward a Soviet-era memorial in the city's Tiergarten park.
A separate rally organized by regional Protestant churches was billed as a "stroll for worldly openness and tolerance" from the Brandenburg Gate to the city's central Gendarmenmarkt square. Some 3,000 gathered on the square, accordng to police.
Regional bishop Markus Dröge said a tolerant Berlin stood for the principles of Germany's post-war constitution and against attempts to split society. Germany's diverse population, drawn from various origins, was a success story for Europe, he said.
Former German Protestant church head Margot Käßmann said she rejected claims by various groups propagating anti-foreigner sentiment that they were defending the so-called Christian Occident (Western world).
Refugees were welcome. Christians, Jews and Muslims could live in peace, she said.
Right-wing and populist groups had in advance registered 5,000 participants for their march near government offices under the slogan "Merkel must go." But, only a thousand turned up, said police. A similar rally in March drew 3,000.
Merkel defends media
Chancellor Merkel, in her weekly video address, defended German media and rejected the right's usage of the derogatory word "Lügenpresse," (lying media).
Since 2014, it has often been directed at reporters and photographers from print and broadcast media by supporters of an upstart anti-Islam party and a parallel movement - Alternative for Germany (AfD) and Pegida.
"I believe that this sweeping condemnation does not fit at all," Merkel said.
The quality of German newspapers, compared internationally, was "very good," she said, adding that they published many "well-researched" items.
Local newspapers were indispensible, she stressed, saying they were in no way obsolete and had a "very important" role to play as they evolved into online, digital editions.
Press freedom 'very important'
It was vital to protect press freedom and value it as "a really important corner pillar of our democratic living-together," Merkel said, while adding that media outlets must always ask themselves whether their coverage included all opinions and reached out to recipients.
The government's task was to ensure media diversity through the best-possible framework conditions, she added, including ways to bring young people into contact with newspapers.
Merkel ran into criticism recently for referring a satirist's lewd remarks about Turkish President Recep Tayyip Erdogan to German prosecutors.
ipj/jm (epd, Reuters, dpa, KNA)