One man has been killed and three injured in a knife attack near Munich that police said appeared to have an Islamist motive.

A 27-year-old German national stabbed four passengers at the railway station at Grafing, a commuter town about 20 miles southeast of Munich, at around 5am local time.

Witnesses told police that the attacker shouted "Allahu Akbar", meaning "God is Greatest" in Arabic.

A spokesperson for the prosecutor's office said that the exact words of the perpetrator have not yet been determined, but, "The assailant made remarks at the scene of the crime that indicate a political motivation – apparently an Islamist motive."

The assailant has been arrested.

A 50-year-old from the town of Wasserburg died of stab wounds in hospital shortly after the attack. The other stabbed men, aged 43, 55 and 58, sustained lighter injuries, police said.

Germany, which is playing a supporting role in the fight against Islamic State, has not suffered a major attack by Islamist militants on the scale of those that have hit neighbouring France and Belgium.

However, ministers have repeatedly warned an attack is possible and German security services are on alert.

More than 800 home-grown radicals have left Germany to join jihadist groups in Syria and Iraq and about 260 have returned.

Germany has also been a transit country for militants who carried out attacks in Belgium this year and Paris last year. There are concerns that some of the more than one million migrants who arrived in the country last year have slipped off officials' radar.

Mayor of Grafing, Angelika Obermayr, condemned today's attack.

She told Sueddeutsche Zeitung: "The idea that people get on an S-Bahn train on a beautiful morning or do their paper round and then become victims of a maniac is terrible," she said.

Additional reporting by Reuters.