Matthew briefly reached the top hurricane classification, Category 5, and was the strongest Atlantic hurricane since Felix in 2007.
The U.S. National Hurricane Center in Miami said Matthew's winds had slipped slightly from a peak of 160 mph (260 kph) to a still-potentially devastating 150 mph (240 kph), a Category 4 storm. It was expected to near eastern Jamaica and southwestern Haiti on Monday.
The latest forecast had Matthew's path passing closer to Haiti than before and the center issued a hurricane warning for Jamaica and "much of Haiti," and said life-threatening rainfall was expected in parts of the impoverished Caribbean nation.
The forecast track would also carry Matthew across Cuba and into the Bahamas, with an outside chance of a brush with Florida, though that would be several days away.
"It's too early to rule out what impacts, if any, would occur in the United States and Florida," said Dennis Feltgen, a spokesman at the Hurricane Center.
As Matthew skimmed past the northern tip of South America there were reports of at least one death - the second attributed to the storm.
Authorities in the area overall breathed a sigh of relief as the storm triggered heavy flooding in towns along the La Guajira peninsula of Colombia, but damage overall was minimal. Some officials were even grateful for the rain after a multi-year drought in the poverty-stricken area.
"Families that evacuated are returning to their homes," said La Guajira Gov. Jorge Velez. "The dikes and wells filled up, the earth is moist, and this benefits agriculture in an area where it hasn't rained for five years, benefiting the community."
Authorities say that at least 27 houses were damaged and two roads were washed out. One person, a 67-year indigenous man, was carried away to his death by a flash flood in an area where it hadn't rained for four years.
Elsewhere, all across Colombia's Caribbean coastline, authorities have set up emergency shelters, closed access to beaches and urged residents living near the ocean to move inland in preparation for storm surges that they said will reach their most-intense moment sometime Saturday.
There's also concern that heavy rain across much of the country this weekend could dampen turnout for a nationwide referendum Sunday on a historic peace accord between the government and leftist rebels.
In Jamaica, high surf began pounding the coast and flooding temporarily closed the road linking the capital to its airport. Carl Ferguson, head of the marine police, said people were starting to heed calls to relocate from small islands and areas near rural waterways.
Residents of the capital, Kingston, crowded supermarkets to buy bottled water, canned food and batteries, and there was already flooding in the coastal town of Port Royal, where officials were urging residents to seek refuge in government shelters once they open up on Sunday.
Many Jamaicans also began stocking up for the emergency.
At the Azan Super Centre, a supermarket in Kingston, shoppers were scooping up flashlights and gas lamps and other key supplies along with food. The kerosene was already sold out.
"It has been chaos from the morning," owner Melain Azan said.
Shopper Nardia Powell said she was stocking up because she learned a hard lesson when she was unprepared for Hurricane Ivan in 2004, as were many others. "So, I just want to be on the safe side, right?" she said.
Feltgen said storm force winds and rain will arrive well before the center of the storm. Jamaicans "basically have daylight today, they have tonight and they have daylight tomorrow to take care of what needs to be done," he said.
Jamaicans are accustomed to intense storms, but Hurricane Matthew looked particularly threatening. At its peak, it was more powerful than Hurricane Gilbert, which made landfall on the island in September 1988 and was the most destructive storm in the country's modern history.
In Haiti, civil protection officials broadcast warnings of a coming storm surge and big waves, saying the country would be "highly threatened" from the approaching system. They urged families to prepare emergency food and water kits.
Emergency management authorities banned boating starting Saturday, particularly along the impoverished country's southern coastline.
Forecasters said rainfall totals could reach 10 to 15 inches (25 to 38 centimeters) with isolated maximum amounts of 25 inches (63 centimeters) in Jamaica and southwestern Haiti.
The U.S. Navy base at Guantanamo Bay, Cuba, is also potentially in the path of the storm. A mandatory evacuation of non-essential personnel, including about 700 family members of military personnel was underway and everyone remaining behind was being told to take shelter, said Julie Ann Ripley, a spokeswoman. There are about 5,500 people living on the base, including 61 men held at the detention center.
As of 8 p.m. EDT (0000 GMT), the storm was centered about 360 miles (580 kilometers) south-southwest of Port-au-Prince, Haiti. It was stationary.
Matthew caused at least one death when it entered the Caribbean on Wednesday. Officials in St. Vincent reported a 16-year-old boy was crushed by a boulder as he tried to clear a blocked drain.