(CNN) -- Tropical Storm Isaac continued its westward path Wednesday, placing officials on alert from Puerto Rico to Guantanamo Bay to Florida, where it could pose a threat to the GOP convention next week.
It's too early to tell what effects Isaac will have on the U.S. mainland. But several computer models bring the storm into the Gulf of Mexico, while others move it farther east over Florida.
With roughly 50,000 people headed to Tampa for the Republican National Convention starting Monday, there is heightened interest in the path of the storm.
"We're monitoring the situation very closely," convention spokesman Kyle Downey said. "We are working closely with state, federal and local officials and plan on putting on a great convention."
Tampa Mayor Bob Buckhorn said his city is prepared.
"We have contingency plan after contingency plan," he said. "We are ready in the event that it happens. I don't think it's going to be a factor in this particular convention. But we are prepared in the event that it is."
At the U.S. naval base at Guantanamo Bay, Cuba, officials canceled the pretrial arguments scheduled to get under way in the trial of Khalid Sheikh Mohammed and four others.
Mohammed -- who has been held since 2006 -- is facing charges related to the September 11, 2001, terrorist attacks.
Pentagon officials said all court events at Guantanamo were canceled because of the potential hurricane. All detainees have been moved to buildings that can withstand such a storm, and those who flew in for the hearing went back home.
At 8 p.m. ET Wednesday, Isaac was about 65 miles (110 kilometers) southwest of Guadeloupe in the Leeward Islands, with maximum sustained winds of 45 mph (72 kph). The storm was moving west at 21 mph, the National Hurricane Center in Miami said.
Tropical storm warnings cover much of the Leeward Islands, as well as Puerto Rico and the Virgin Islands.
Dominican officials issued a hurricane warning along the nation's southern coast.
A hurricane watch was in effect for Haiti, Puerto Rico and the U.S. Virgin Islands, which means hurricane conditions are possible.
"Some strengthening is forecast during the next 48 hours, and Isaac could become a hurricane Thursday night or Friday," the hurricane center said.
The center of the storm was moving through the Leeward Islands on Wednesday evening and was expected to pass near or south of the Virgin Islands and Puerto Rico on Thursday, before approaching the Dominican Republic on Thursday night and into Friday.
Isaac could bring 4 to 8 inches of rain over the Northern Windward Islands and the Leeward Islands, the center said, and up to 6 inches of rain in some parts of Puerto Rico.
On the island of Hispaniola, home to the Dominican Republic and Haiti, 8 to 12 inches of rain, with maximum amounts of 20 inches, are possible, the center said.
Puerto Rico Gov. Luis Fortuno said the U.S. commonwealth has as many as 433 shelters ready to be activated by local mayors as the storm approaches. He said he expects rain from the system to reach Puerto Rico on Wednesday.
Aid organizations were keeping an eye on Haiti, where hundreds of thousands still live in camps after the deadly 2010 earthquake.
According to the U.N. High Commissioner for Refugees, 421,000 people are in camps in and around Port-au-Prince.
Isaac could be the first significant storm to hit Haiti since the devastating earthquake. Tropical Storm Emily threatened in 2011, but it weakened before hitting western Haiti.
"We watch those storms every single time they come near because Haiti is so vulnerable," said Amy Parodi, a spokeswoman for the Christian humanitarian organization World Vision.
The agency has met with the government in previous summers to discuss contingency plans for major storms, and pre-positioned relief items are available, she said.
Forecasters caution that the forecast track is uncertain and that the storm could be anywhere from the Bahamas to the north and the Cayman Islands to the south on Sunday.
CNN's Dave Alsup, Allison Brennan, Kevin Liptak, Jason Hanna, Brad Lendon, Dave Hennen and Sean Morris contributed to this report.