MADRID — Spain’s prime minister on Saturday rejected a request by the leader of Catalonia to approve a referendum that would allow the northeastern region to decide whether to secede from the rest of the country.

In a written reply, Prime Minister Mariano Rajoy told Artur Mas, leader of the economically powerful region, that “the ties that bind us together cannot be undone without enormous cost” and that the two politicians should hold talks instead.

Mr. Rajoy’s answer officially rebuffed the pro-separatist request that Mr. Mas made in July. Spain’s Constitution says only the central government can call a referendum.

More than one million people showed support for Catalan independence on Wednesday by joining hands to form a 250-mile human chain across the region.