A video broadcast by Spanish television stations showed the car crashing off the tree-lined road in a cloud of dust in the northwestern town of Carral during the A Coruna Rallyn yesterday.
"One of the cars in the rally left the road and ran down various spectators" as it sped around a bend about 8:00pm (1800 GMT), a spokesman for the Civil Guard police force told AFP.
"We have confirmed that six people died, four woman and two men. One of them was a pregnant woman," said the spokesman, who asked not to be named.
The spokesman said authorities were investigating the crash.
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The rally cars "go too fast for that kind of road. They are normal roads and people stand on the edge of the bend" to get a better view, he said.
Spanish media reported that the car was a compact Peugeot 206 XS and that children were among the injured. The drivers were not reported to have been hurt.
Spain's state Higher Sports Council said in a Twitter message that it "deeply regrets the accident in the A Coruna Rally. Our condolences to the families and friends of the deceased."
In March a co-driver was killed in the Mallorca Classic Rally after reportedly crashing into a tree on the Spanish island.