Police in the eastern German city of Halle launched at least 10 criminal inquiries on Tuesday after a demonstration during which protesters used Nazi slogans and displayed Nazi symbols.

Police say they are also investigating incidents in which some protesters attacked police but did not give further details.

About 450 marchers joined the protest on Monday night, part of a series of demonstrations across eastern Germany after recent incidents in the cities of Chemnitz and Koethen in which Germans have died after encounters with asylum seekers.

Most of the marches have been protests against the presence of migrants, whose numbers have risen dramatically in Germany since 2015, when the government opened Germany's borders to people fleeing conflict.

There is concern that the anti-migrant movement is becoming a breeding ground for neo-Nazi sentiment.

Police said they are investigating cases where marchers displayed symbols of banned organizations, performed Nazi salutes or called out "Sieg Heil" (Hail Victory), a phrase commonly used by the Nazis.

Authorities said many of those marching appeared drunk.

But they were quick to point out that they could not say if all the people marching in Halle belonged to right-wing groups. They also noted that a peaceful counter-demonstration drew in 80 to 100 participants.

Similar police probes after rallies in Chemnitz will see two men separately stand trial on Thursday and Friday, a court spokeswoman said.

The men, aged 33 and 34, are both accused of having performed Nazi salutes during rallies in Chemnitz on August 27 and September 1.