A dozen people were killed and at least 10 seriously injured after a Polish bus carrying 57 pilgrims veered off a motorway in eastern Hungary, in an accident that a survivor described as "unimaginable".

Hungarian Prime Minister Peter Magyar said on Sunday in a Facebook post that the bus had run into a ditch and tipped over, at around 1:00 am.

The bus, which also had two drivers on board, was returning to Poland from a shrine to the Virgin Mary at Medjugorje in southeastern Bosnia.

The injured were taken to hospitals in four nearby cities.