The Islamic State group claimed responsibility Tuesday for a deadly shooting rampage in Vienna the day before, the group said in a statement on its Telegram channels.

The statement on the messaging app identified "a soldier of the caliphate" as being responsible for the assault on Monday night in the Austrian capital that left four people dead.

In a separate statement, accompanied by a photograph of the armed assailant, IS propaganda arm Amaq cited "a gun attack yesterday (Monday) by an Islamic State fighter in the city of Vienna".

Amaq also published a short video in which the armed perpetrator filmed himself pledging allegiance to the head of the jihadist organisation.

Austrian police had said earlier Tuesday that the shooting had been carried out by a known Islamist extremist who had spent time in prison.

Twenty-year-old Kujtim Fejzulai was shot dead after he opened fire with an automatic weapon in a busy area of the historic Austrian capital.

Austrian security forces swooped on 18 different addresses, including Fejzulai's home, and made 14 arrests as they looked for possible accomplices and sought to determine if he had acted alone.  

The attack came after several Islamist atrocities in France in recent weeks, including an assault on church-goers in the Mediterranean city of Nice.

IS jihadists declared a "caliphate" in large swathes of Syria and neighbouring Iraq in 2014, implementing their brutal interpretation of religion on millions under their rule.

But various campaigns against them in both countries whittled away the proto-state, and they were expelled from their last patch of territory last year in Syria's east.

The group has continued to claim deadly attacks in Syria and Iraq, as well as Afghanistan and West Africa.

IS also claimed responsibility for an attack Monday in Afghanistan on Kabul University that killed 22 people.