In Haiti, the government and international aid groups announced plans to evacuate several thousand people from one of the settlement camps that sprang up in the aftermath of the 2010 earthquake.
Isaac was expected to dump eight to 12 inches of rain on the island of Hispaniola that is shared by Haiti and the Dominican Republic.
"That kind of rain is going to cause some life-threatening flash floods and mudslides," said Dennis Feltgen, a spokesman for the Hurricane Center in Miami.
Isaac was centered about 135 miles south-southeast of Port-au-Prince, the Haitian capital, on Friday afternoon, and its maximum sustained winds had held steady at 60 mph. It was moving west at 14 mph, according to the Hurricane Center.
The center of the storm was expected to pass over Haiti Friday night.
Tropical force winds extend nearly 200 miles beyond the storm's center.
In flood-prone Haiti, Prime Minister Laurent Lamothe urged people to avoid crossing rivers, to tape their windows, and to stay calm, saying "panic creates more problems."
Lamothe and other Haitian officials said the government had set aside about $50,000 in emergency funds and had buses and 32 boats on standby for evacuations.
But among many Haitians, the notion of disaster preparedness in a country where most people get by on about $2 a day was met with a shrug.
"We don't have houses that can bear a hurricane," said Jeanette Lauredan, who lives in a tent camp in the crowded Delmas district of Port-au-Prince.
About 400,000 people remain in settlement camps comprised of shacks and tarps in the wake of Haiti's devastating 2010 earthquake.
In the Haitian capital of Port-au-Prince, people went to work as usual, but commercial banks closed at noon and some residents took precautions as the sky darkened, rain began and the wind picked up.
"Just in case this gets very bad the sky is turning gray I'm making sure we have enough food in the house," said 25-year-old Joanne Dorville as she carried home rice, sardines, black beans and cooking oil she had purchased in a street market.
Haitian authorities and aid workers from the International Organization for Migration and the Haitian Red Cross sought to evacuate as many as 8,000 people from a tent camp at the edge of the capital, but no one accepted Friday morning. Two school buses that were supposed to shuttle the people to temporary shelters drove away empty.
"If I leave for a shelter, by the time I come back, everything I have will be gone," said Charles Delizaire, a 39-year-old resident of the settlement named Marassa.
So far, Isaac itself had caused no reported injuries or deaths, but police in Puerto Rico said a 75-year-old woman died near the capital of San Juan on Wednesday when she fell off a balcony while filling a drum with water in preparation for the storm.
In the Dominican Republic, authorities began to evacuate people from low-lying areas but, as in Haiti, they encountered resistance.
"Nobody wants to leave their homes for fear they'll get burglarized," said Francisco Mateo, community leader of the impoverished La Cienaga neighborhood in Santo Domingo, the capital.
However, authorities said they have managed to evacuate nearly 2,900 people. The majority were transferred to the homes of relatives while about 300 were sent to government shelters.
Local forecasters said they expect the storm to dump up to 12 inches of rain through Saturday, causing possible flooding and landslides.
"That's a lot of water," said Juan Manuel Mendez, emergency operations director. "The worst is yet to come."
Two airports in Santo Domingo reopened, although the country's remaining seven airports remained closed, authorities said.
Blake, the U.S. forecaster, said that while Isaac hadn't strengthened much in the Caribbean, it could gain power as it moves away from Cuba. "When it moves back over water, it has a chance to restrengthen," he said.
Commercial airlines, including American Airlines, canceled flights to and from the Dominican Republic, Haiti and Puerto Rico.
Organizers of next week's Republican National Convention in Tampa said they were working closely with state and federal authorities on monitoring storm as they prepared for the arrival of 70,000 delegates, journalists and protesters, and Florida Gov. Rick Scott said there were no plans to cancel the convention.
Out in the eastern Atlantic, another tropical storm, Joyce, was downgraded to a tropical depression late Thursday, and posed no threat to land. The hurricane center in Miami said Joyce had maximum sustained winds of 35 mph and that it was becoming disorganized.