PORT-AU-PRINCE, Haiti — An extremely dangerous Hurricane Matthew moved slowly over the Caribbean on Sunday following a track that authorities warned could trigger devastation in parts of Haiti.

The powerful Category 4 hurricane had winds of 145 mph at late afternoon and the center was expected to pass across or very close to the southwestern tip of Haiti late Monday before reaching Cuba on Tuesday, the U.S. National Hurricane Center in Miami said.

A hurricane warning was in effect for Jamaica, Cuba and Haiti. Forecasters said the southern Haitian countryside around Jeremie and Les Cayes could see the worst of it.

“Wherever that center passes close to would see the worst winds and that’s what’s projected to happen for the western tip of Haiti,” said John Cangilosi, a hurricane specialist at the U.S. center. “There is a big concern for rains there and also a big concern for storm surge.”

Matthew is one of the most powerful Atlantic hurricanes in recent history and briefly reached the top classification, Category 5, becoming the strongest hurricane in the region since Felix in 2007. The hurricane center said the storm appeared to be on track to pass east of Florida through the Bahamas, but it was too soon to predict with certainty whether it would reach the U.S. coast.

Officials with Haiti’s civil protection agency said there were roughly 1,300 emergency shelters across the country, enough to hold up to 340,000 people. Authorities broadcast warnings over the radio telling people to swiftly heed evacuation warnings, trying to counter a common tendency for people to try to stay in their homes to protect them during natural disasters.

In a Sunday address carried on state radio, interim President Jocelerme Privert urged Haitians to listen closely to the warnings of officials and be ready to move at a moment’s notice.

Forecasters said the slow-moving hurricane was expected to dump 15 to 25 inches of rain over southern Haiti.