At 2 p.m. EDT, the Category 2 storm with maximum sustained winds of 100 mph (160 kph) was centered about 55 miles (95 kilometers) west-southwest of Cuba's western tip, hours after brushing past Mexico's Yucatan Peninusla and the islands of Cozumel and Isla Mujeres.
Mexican authorities said American Mickey Goodwin, 54, of Corpus Christi, Texas, drowned Tuesday while swimming off a Cancun beach after he ignored warnings and red flags alerting to dangerous waters, the only fatality reported so far.
The U.S. National Hurricane Center said Paula was stationary early Wednesday afternoon and expected to begin heading north-northeast near 5 mph (7 kph) later in the day, its small core forecast to be near or moving over western Cuba late Wednesday or early Thursday.
Forecasters said Paula, despite some expected weakening, threatened a storm surge and anywhere between 3 and 6 inches of rainfall on parts of Cuba. The storm was small in area, with hurricane force winds extending just 15 miles (30 kilometers) from its center.
Cuba's chief meteorologist, Jose Rubiera, said Paula was expected to take a trajectory slightly north of previous projections.
"The hurricane's intensity ought to diminish as it approaches Cuba, which is obviously good news," Rubiera told his countrymen in a special broadcast on state-run television. "This is an extremely small hurricane."
In Pinar del Rio, many residents shuttered themselves indoors as heavy rain began falling. Veterinarian Humberto Rodriguez and his 13-year-old daughter, Maria, made their way slowly in a horse and buggy down a highway near the town of Los Palacios, heading to their home in nearby Consolacion del Sur.
"I'm evacuating my daughter from boarding school and we're going home to prepare," said Rodriguez, 48, as the girl rested her head on a pillow. "I hope this one will not be as strong as the others."
Rubiera said there was still a chance Cuba could be spared the brunt of Paula's force if it continued to drift north faster than anticipated.
Nonetheless, Cuban officials were taking no chances.
The communist government activated the island's crack Civil Defense forces and urged residents in western Pinar del Rio province and on the Isla de la Juventud to cover up windows with plywood, tie down loose items and stay vigilant for flooding and heavy rains. No evacuations were ordered.
Pinar del Rio was devastated by three hurricanes that hit the area and other parts of Cuba in 2008, doing about $10 billion in damage. The area is known for its high-quality tobacco fields and is crucial for Cuba's famed cigar industry. Growers had planned to begin planting tobacco on Tuesday ahead of next year's harvest.
Hurricane specialist Robbie Berg at the National Hurricane Center in Miami noted that small hurricanes can be more unpredictable and the fact that Paula slowed and paused for a time Wednesday could actually raise the threat of heavy rainfall.
"Small storms are a little more volatile. They can strengthen more rapidly and weaken more rapidly so they are a little more unpredictable," Berg told The Associated Press. "Whenever a storm is moving slower it's going to spend a longer time over any particular area, dumping heavy rain," Berg said.
"Right now, western Cuba is under the gun."
Berg said the middle and lower Florida Keys are under a tropical storm watch even though no U.S. landfall is forecast at this time.
As the storm left Mexican territory Wednesday, there were no immediate reports of major problems in Cancun or other resort areas with an estimated 27,000 tourists in the October off-season.
"We can declare the coasts completely out of danger," Mexico's Quintana Roo Gov. Felix Gonzalez said as transportation links resumed there.
On Tuesday, heavy rains and high winds destroyed 19 homes in northeastern Honduras, that country's emergency authorities said.
Associated Press reporter Gabriel Alcocer in Cancun, Mexico and AP television producer Fernando Gonzalez in Pinar del Rio, Cuba contributed to this report.