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 vicinity of the two officers.

Rival protests held over killing of German citizen Far-right and anti-fascist groups clashed in eastern German city of Chemnitz Saturday over alleged killing of a man by migrants.More than 4,500 far-right protestors attended the anti-immigration rally organized by the Alternative for Germany (AfD) party and the Pro Chemnitz group, a week after a 35-year-old German citizen was allegedly killed by two migrants after a street row.The protestors, carrying banners that demanded immediate deportation of illegal migrants, chanted slogans “Merkel must go”, “Resistance” and “We are the people”.Leftist and anti-fascist groups organized a counter demonstration to protest the far-right violence in Chemnitz, as mobs were randomly attacking foreign-looking people on the streets in recent days.The counter-protest drew at least 3,500 people, according to the organizers.Authorities maintained a heavy police presence and tried to keep rival groups apart in a bid to avoid violence.However, the clashes between right-wing extremists and leftist groups left at least 11 people injured.

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.

Far-right protests continue in eastern Germany Around a thousand far-right demonstrators rallied in the eastern German city of Chemnitz Thursday after days of violent protests.The protesters shouted slogans against Chancellor Angela Merkel’s open-door policy for refugees, demanded immediate deportation of illegal migrants and attacked the media, chanting the Nazi-era term “Luegenpresse" (lying press).They also carried banners bearing the messages “We are the people”, “For security and order” and “The people are rising up”.Unrest in the city begun Sunday following reports on social media that attributed the killing of a 35-year-old German citizen to two migrants from Syria and Iraq.Far-right extremists took to the streets, and some of them randomly attacked foreign-looking people, including an Afghan, a Syrian and a Bulgarian man, according to police.The far-right group Pro Chemnitz, which organized Thursday’s demonstration, has announced that they will continue their protests with another major rally scheduled for Saturday.Several leftist groups also announced that they would hold a counter protest on the same day in Chemnitz.Germany condemns far-right demo in eastern city after fatal disputeGermany slams US President Trump’s sanctions policyRacism in Germany ‘must be taken seriously,’ says Merkel after Özil debate

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 organised 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.