BERLIN (Reuters) - Germany’s far-right Alternative for Germany (AfD) has overtaken the center-left Social Democrats (SPD), a poll showed on Tuesday, days after some of the most violent protests by radical right-wingers the country has seen in decades.

FILE PHOTO: Germany's anti-immigration party Alternative for Germany (AfD) co-leader Joerg Meuthen delivers a speech at the traditional Gillamoos festival in Abensberg, Germany, September 3, 2018. REUTERS/Andreas Gebert

Some 6,000 supporters of the AfD and anti-Islam PEGIDA joined protests in the eastern city of Chemnitz on Saturday, following other demonstrations last week, after a fatal stabbing on Aug. 26. Two immigrants were arrested for the killing.

An INSA opinion poll on Tuesday put the AfD up half a percentage point at 17 percent, with the SPD, who share power with Chancellor Angela Merkel’s conservatives, slipping by the same amount to 16 percent. Merkel’s conservative bloc was on 28.5 percent.

Germany’s next electoral test comes on Oct. 14 when Merkel’s Bavarian allies face a major challenge from the AfD for state government.

The AfD, the third-biggest party in last year’s election and the main opposition, seized on the killing of a 35-year old German in Chemnitz and the subsequent arrests of a Syrian and Iraqi to ramp up criticism of Merkel’s open-door asylum policy.

Prosecutors said on Tuesday they were looking for a third suspect and Der Spiegel reported there was some doubt about the identity of the two already under arrest.

Merkel, who has been criticized for remaining largely silent during days of protests, plans to visit the city, a spokesman said. No date for the visit has been set.

Images showed skinheads at last week’s protests chasing migrants through the streets, hurling bottles and fireworks, and making Nazi salutes, illegal in Germany.

Calls have mounted for the domestic intelligence agency to place the AfD under surveillance.

Bjoern Hoecke, an AfD leader from the state of Thuringia who has criticized Germany’s main memorial to the victims of the Holocaust as a “monument of shame” and wants Germany to re-write its history books, took part in Saturday’s march in Chemnitz.

In a show of resistance, some 65,000 people attended a rock concert “against xenophobia” on Monday night in Chemnitz, given by mostly left-leaning groups.