German police shot dead a 17-year-old Afghan refugee Monday after he attacked train passengers with an axe and a knife, seriously wounding four in what one official said was a "probable" Islamist attack.

Several other people were also injured in the assault on a regional train near the southern city of Wuerzburg, police said, adding that the teenager was killed as he tried to flee.

Joachim Herrmann, the interior minister of Bavaria state, said the assailant had arrived as an unaccompanied minor in Germany and had lived at first in a shelter and then more recently with a foster family in nearby Ochsenfurt.

"It is quite probable that this was an Islamist attack," said a ministry spokesman, adding that the assailant had shouted "Allahu akbar" (God is greatest).

However he stressed that the investigation was ongoing and that the teenager appeared to have acted alone.

The attack happened around 9:15 pm (1915 GMT) on the train, which runs between Treuchlingen and Wuerzburg in Bavaria.

Four people were reported seriously injured and one other lightly injured. Fourteen people were treated for shock.

An eyewitness who lives next to the railway station told DPA news agency that the train, which had been carrying around 25 people, looked "like a slaughterhouse" after the attack, with blood covering the floor.

The man, who declined to give his name, said he saw people crawl from the carriage and ask for a first-aid kit as other victims lay on the floor inside.

"The perpetrator was able to leave the train, police left in pursuit and as part of this pursuit, they shot the attacker and killed him," a police spokesman said.

Hermann later said that the teenager was shot when he attacked police while trying to escape the scene.

A special police force unit happened to be nearby and was able to mobilise quickly, Hermann added.

Germany has thus far escaped the kind of large-scale jihadist attacks seen in the southern French city of Nice last week, in which 31-year-old Mohamed Lahouaiej Bouhlel used a truck to mow down people leaving a Bastille Day fireworks display, killing 84 people. The attack was claimed by the Islamic State group.

In May in Germany, a mentally unstable 27-year-old man carried out a knife attack on a regional train in the south, killing one person and injuring three others.

Early reports suggested he had yelled "Allahu akbar" but police later said there was no evidence pointing to a religious motive. He is being held in a psychiatric hospital.

- Political tensions -
Germany let in a record nearly 1.1 million asylum seekers last year, with Syrians the largest group followed by Afghans fleeing ongoing turmoil and poverty in their country.

However the number of refugees arriving in Germany has fallen sharply as a result of the closure of the Balkans migration route and an EU deal with Turkey to stem the flow.

In April, May and June, the number was around 16,000 each month, less than a fifth of the tally seen at the start of the year, according to official figures.

Bavaria is governed by the Christian Social Union (CSU), sister party to Chancellor Angela Merkel's conservative Christian Democrats.

The CSU has been loudly critical of Merkel's welcoming stance toward asylum seekers, a split that threatened the unity of the ruling coalition in Berlin and sent the government's approval ratings plunging.

It has also lent support to a right-wing populist party, Alternative for Germany, which was founded as a eurosceptic protest outfit in 2013 but now mainly rails against Islam and Germany's refugee influx.

It currently polls at around 10 percent and is represented in half of Germany's 16 states as well as the European Parliament.

Merkel's popularity has rebounded recently but the attack in Bavaria is likely to revive political tensions.