Four attacks in a week, three of them committed by asylum seekers and two claimed by the Islamic State group, left Germany shaken and prompted renewed criticism on Tuesday of Chancellor Angela Merkel's open-door migration policy.

Horst Seehofer - premier of Bavaria, where three of the attacks took place, and one of the most vocal critics of Merkel's refugee policies - said that the government should reverse its decision not to deport criminal migrants to conflict zones.

"We must seriously reconsider how to treat these people going forward, particularly if their behaviour falls foul of the law, or if they represent a danger," Seehofer told Munich newspaper Muenchner Merkur's Tuesday edition.

An Islamic State-claimed suicide attack in the Bavarian town of Ansbach late Sunday, a deli knife attack in nearby Reutlingen on the same day and an axe-and-knife attack on a Bavarian commuter train earlier in the week were all committed by recent immigrants.

The debate about how to deal with criminal migrants, which first flared up in January after a spate of sexual assaults against women in Cologne, reached new levels on Tuesday amid suggestions for tougher screening of refugees and plans to boost the police force.

Thomas Strobl, the interior minister of Baden-Wuerttembuerg, where the deli knife attack took place, also demanded a tougher stance against refugees.

"The rising number of migrants has coincided with a rise in the absolute number of crimes committed by this group of people," Strobl told Funke media group, adding that this should not result in blanket suspicion of refugees.

A failed Syrian asylum seeker blew himself up outside a music festival venue in Ansbach late Sunday with a backpack laden with explosives and shrapnel, injuring 15 people.

The 27-year-old was denied asylum in Germany in late 2014. He had been due for deportation to Bulgaria, the first EU country he registered in, but officials said that process was suspended because of the man's psychological instability.

Islamic State posted a video early Tuesday via its mouthpiece, Aamaq News Agency, in which a man claiming to be the attacker said he would carry out a "martyrdom ... in response to the crimes being committed by the coalition, with Germany, in bombing men, women and children."

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