The Cuban police detained several dissidents on Tuesday and thwarted an unauthorized political protest in the most significant crackdown on the opposition since Cuba and the United States agreed this month to normalize ties. The State Department condemned the detentions, in which about 12 people, including the husband of the opposition blogger Yoani Sánchez, were taken away by the police. Several other dissidents were told not to leave their homes as police officers parked outside, said Elizardo Sánchez, leader of a dissident rights group. The detentions stopped a planned open microphone event at Revolution Square in Havana. The event’s organizer, Tania Bruguera, a performance artist, was missing, and her associates said they presumed that she, too, had been detained.