SAN JUAN, Puerto Rico — Tropical Storm Isaac churned toward the Dominican Republic and Haiti on Thursday, threatening to strengthen into a hurricane that could take a shot at Florida just as the Republicans gather for their national convention.

The storm dumped heavy rain across eastern and southern Puerto Rico and whipped up waves as high as 10 feet (3 meters) in the Caribbean as it moved through the region.

U.S. forecasters said Isaac could become a Category 1 hurricane Friday as it approaches the island of Hispaniola, which is shared by the Dominican Republic and Haiti. It was expected to weaken a little while crossing over Haiti and the eastern two-thirds of Cuba.

The storm was projected to head toward Florida as a hurricane by Monday, but the U.S. National Hurricane Center in Miami said some forecast models predict it could go farther west into the Gulf of Mexico, so "significant uncertainty remains about the threat Isaac poses to Florida."

Isaac was centered 180 miles (285) kilometers south-southwest of San Juan, Puerto Rico, late Thursday afternoon, with maximum sustained winds of 40 mph (65 kph). It was moving west-northwest at 16 mph (26 kph), according to the hurricane center.

Haitian Prime Minister Laurent Lamothe urged people to avoid crossing rivers and to tape their windows, and said they should ask relatives overseas to wire money so they can stock up on food and water.

Above all, he said, it was important to stay calm. "Panic creates more problems," he said.

Lamothe and other officials in Haiti, which is prone to flooding, said that the government has set aside about $50,000 in emergency funds and that it had buses and 32 boats on standby for evacuations.

While Haiti's government spent the day preparing for Isaac, others did not because they didn't have the means. The notion of preparation in a country where the bulk of the population gets 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, stretching out her arms in concern.

About 400,000 people remain in settlement camps that are mere clusters of shacks and tarps as a result of Haiti's devastating 2010 earthquake.

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.

Schools and government offices remained closed Thursday on the U.S. territory, where Gov. Luis Fortuno said 7,800 people were without power and more than 3,000 had no water.

With rain falling on and off throughout the day, the governor warned Puerto Ricans to stay away from beaches and swollen rivers.

"It's not the day to participate in recreational activities in these areas," Fortuno said.

Jose Alberto Melendez, 51, disregarded the advice and went to a beach near Old San Juan.

"It's my birthday," he said. "I had already planned to come to the beach."

He unfolded his chair and turned on the radio just as a squall approached, sending him running for shelter.

Nearby, a group of four friends visiting from Poland picked up their beach blankets and took cover as well.

Agata Gajda, 24, said she and her three friends had slept on the beach because there was no room at a hostel. She said police woke them up Thursday morning and warned them about the storm.

In the Dominican Republic, authorities began to evacuate people living in low-lying areas but encountered some resistance.

"Nobody wants to leave their homes for fear they'll get robbed," said Francisco Mateo, community leader of the impoverished La Cienaga neighborhood in Santo Domingo, the capital.

The approach of the storm led military authorities at the U.S. base in Guantanamo Bay, Cuba, to cancel pretrial hearings for five prisoners charged in the Sept. 11 attacks. They also evacuated about 200 people, including legal teams and relatives of Sept. 11 victims.

Isaac also posed a threat to next week's Republican National Convention in Tampa, where 70,000 delegates, journalists and protesters are expected to descend on the city.

Convention officials said they were working closely with state and federal authorities on monitoring the storm.

"We continue to move forward with our planning and look forward to a successful convention," convention CEO William Harris said in a statement.

Florida Gov. Rick Scott said RNC officials had consulted with state, local and federal authorities and there were no plans to cancel the convention.

Hillsborough County Sheriff David Gee said some outside agencies that had planned to send officers to help with convention security in Tampa might be forced to keep them home to deal with a storm.

"My primary concern right now is that we will lose resources," he said

Out in the eastern Atlantic, another tropical storm, Joyce, formed over the open water, but forecasters said it posed no immediate threat to land. The U.S. Hurricane Center in Miami said that the storm had maximum sustained winds of 40 mph (65 kph) and that it was becoming disorganized.