MIAMI — A weather system in the southwestern Caribbean is expected to develop and strengthen this week, prompting a tropical storm warning for Jamaica and a hurricane watch for the Cayman Islands to be issued Sunday, the National Hurricane Center in Miami said.

The system also could bring heavy rainfall to Cuba and Florida as well as the northern coast of the Gulf of Mexico later this week, the center said.

At 4 p.m. EST Sunday, the system was located about 345 miles (555 kilometers) south of Kingston, Jamaica, with maximum sustained winds of 35 mph (55kph), the center said. It was moving to the northeast at 7 mph (11 kph), with a turn to the north and then northwest expected.

It was expected to become a tropical storm Monday with steady strengthening forecast. A tropical storm is defined as having maximum sustained winds of 39 mph (62.8 kph) up to 73 mph (117.5 kph). Hurricane-force winds are 74 miles (119.1 kph) and greater.

The disturbance was expected to be near Jamaica by late Monday and the Cayman Islands on Tuesday and Wednesday, according to the hurricane center, which urged residents in Cuba and the Florida Keys to monitor the storm’s progress. Heavy rainfall will affect the western Caribbean with totals of 3 to 6 inches (76 to 152 mm), and up to 9 inches (229 mm) expected locally in Jamaica and southern Cuba. Flooding and mudslides are possible in those nations.

Heavy rains will reach Florida and adjacent areas of the southeast U.S. by mid- to late-week, the center said.