Police in Germany's southern state of Bavaria are investigating two officers suspected of performing the illegal Hitler salute.

The German constitution makes it a crime to exhibit Nazi symbols and the incident is likely to feed into a heated debate about racism and the rise of the far right after a record influx of mainly Muslim migrants three years ago.

Police said in a statement on Saturday the two policemen had shouted anti-immigrant remarks and made the salute in a pub in the city of Rosenheim on Thursday. It based its information on a witness who was in the same beer garden as the two officers.

A third man, described as a security guard in the police statement, had also taken part and made the salute. The policemen have been suspended.

German politicians have been urging action to combat a rise in hostility toward foreigners after skinheads last Sunday clashed with police in an eastern city where a man was fatally stabbed and two migrants were identified as the main suspects.

Skinheads raised their arms in Nazi salutes, chased people who appeared to be outsiders and wrestled with police in Chemnitz after police identified the suspects as a Syrian and an Iraqi.

The leaking of the arrest warrant for one of the two stabbing suspects to the anti-Islam group PEGIDA raised concerns that some justice officials in the state of Saxony, where Chemnitz is located, were sympathetic to the far right.

"We will not allow the extreme right to infiltrate our society," Justice Minister Katarina Barley told the Bild am Sonntag newspaper on Sunday, urging authorities in Saxony to investigate far-right groups.

Chancellor Angela Merkel's liberal immigration policy remains deeply divisive in a country that has taken in more than 1.6 million people over the last four years.

The influx contributed to the rise of the Alternative for Germany (AfD) party, which entered parliament for the first time in an election last year with a campaign that proclaimed Islam to be incompatible with the German constitution.

Some 8,000 people took part in a demonstration organized by the AfD and the anti-Islam group PEGIDA in Chemnitz on Saturday. About 3,000 people attended a rival protest by leftist groups.

Police said on Sunday that the demonstrations were largely peaceful.

Leftist groups will hold a concert in the city on Monday to denounce xenophobia and hatred against refugees and foreigners.