The vehicle was carrying students from about 20 countries, many of them on the European Erasmus exchange programme in Barcelona, the seaside capital of Spain's northeastern Catalonia region, regional authorities said.
The driver lost control of the coach which crossed the central reservation and crashed into an oncoming car near the small Catalonian town of Freginals, about 150 kilometres (95 miles) south of Barcelona, just before 6:00am (0500 GMT) on Sunday.
Seven Italians, two Germans, a Romanian, a Frenchwoman, an Austrian and a student from Uzbekistan -- all women aged between 19 and 25 -- died in the crash.
Earlier, he told Spanish radio the victims were "crushed between the coach and the road".
Twenty-four other passengers from 13 different nations remained in hospital on Monday, six of them in serious or critical condition, said Toni Comin, in charge of health in Catalonia.
Alessandro Saracino, the grief-stricken father of one the Italian victims, said it appeared that the driver "fell asleep".