A suspect in German police custody following a stabbing rampage in the city of Solingen that killed three people and injured eight is a 26-year-old Syrian man, authorities said on Sunday as they looked into his possible links with Islamic State.

The suspect turned himself in late on Saturday and admitted to the crime, Duesseldorf police and prosecutors said in a joint statement early on Sunday.

Friedrich Merz, a prominent politician who leads the opposition, centre-right CDU party, said the country should stop admitting further refugees from Syria and Afghanistan.

"It's enough!" he said in a letter on his website.

Hendrik Wuest, premier of the state of North Rhine-Westphalia where Solingen is located, on Saturday described the attack as an act of terror.

Daesh had claimed responsibility on Saturday for the attack, saying that the man  was a "soldier of the Islamic State" in a statement on its Telegram account.

The group also said in the statement that the attack was carried out by one of its members "in revenge for Muslims in Palestine and everywhere".

The incident, along with the group's claim of responsibility, sparked concern among some politicians who urged enhanced security, tighter curbs on weapons, stiffer punishment for violent crimes, and limits to immigration.

The attack occurred during a festival on Friday evening in a market square where live bands were playing to celebrate Solingen's 650-year history. Mourners made a makeshift memorial near the scene.