(CNN)--Miami Beach Mayor Dan Gelber declared a state of emergency and set a curfew Saturday, saying the crowds that have descended on the city recently are "more than we can handle."

"Too many are coming, really, without the intention of following the rules, and the result has been a level of chaos and disorder that is just something more than we can endure," Gelber told CNN's Ana Cabrera.

Police in Miami Beach said early Sunday that they arrested "at least a dozen" people following the start of the curfew.

"Officers began dispersing crowds at 8 p.m. and ultimately achieved a satisfactory level of compliance," police spokesman Ernesto Rodriguez told CNN.

The 8 p.m. curfew and road closures in the city's entertainment district will be in effect for the next 72 hours, Gelber said at a news conference Saturday.

The causeways to Miami Beach from the mainland will be closed to non-local traffic starting at 9 p.m. for the next few nights, Gelber said.