LISBON — A tour bus carrying German tourists crashed on Madeira, a Portuguese island, on Wednesday, killing 29 people and injuring 28 others, the authorities said.

The bus, which was carrying 55 people, rolled down a steep hillside after veering off the road on a bend east of the capital, Funchal, and struck at least one house, Mayor Filipe Sousa told the cable news channel SIC.

Foreign Minister Augusto Santos Silva of Portugal said preliminary reports indicated that all the dead were German. But Tomasia Alves, the head of the Funchal hospital, said that not all the victims had been identified and refused to confirm the nationality of the dead.

Pedro Calado, the vice president of Madeira’s regional government, said at a news conference that the injured, including the Portuguese driver and a local tour guide, were taken to a hospital. It was not clear whether anyone killed was not originally on the bus, such as people on the roadside at the time of the crash.