* 'Thank God for sparing us,' St. Lucia deputy PM says
* Storm could strengthen into hurricane early next week
* Ernesto forecast to hit Mexico's Yucatan Peninsula (Updates storm position, adds quotes, detail)
MIAMI, Aug 3 (Reuters) - Tropical Storm Ernesto swept over the tiny island of St. Lucia on Friday and could strengthen into a hurricane as it races westward across the Caribbean Sea, forecasters said.
All warnings were dropped for the southeastern Caribbean islands by midday. By Friday evening, the storm was over open water about 250 miles (400 km) west of St. Lucia and was not expected to threaten any other islands for the next few days.
Ernesto was forecast to pass south of Jamaica on Sunday and then strengthen into a hurricane before hitting Mexico's Yucatan Peninsula on Wednesday, the U.S. National Hurricane Center said.
The storm had top sustained winds of 50 mph (85 kph) and would become a hurricane if they reach 74 mph (119 kph). It was speeding westward at 21 mph (33 kph) and was forecast to turn more to the northwest next week.
Some computer forecasting models showed the storm moving into the southern Gulf of Mexico by Thursday, but it was too early to know whether it could disrupt oil and gas operations in the Gulf.
Businesses and government offices were ordered closed until noon on St. Lucia as Ernesto passed over the island, churning up 12-foot (3.7-meter) waves a few miles off its north shore.
It moved so quickly that St. Lucia got less than an inch of rain and there were no reports of damage or injuries.
"I want to thank God for sparing us the worst," said Acting Prime Minister Philip Pierre, who is filling in while Prime Minister Kenny Anthony attends the Olympic Games in London.
Pierre said there was still a chance of heavy rains.
"We have to still be cautious in our approach but the all clear has been given and normal business activity can return to St. Lucia," he said.
August and September are usually the most active months of the Atlantic-Caribbean hurricane season, which runs from June 1 to Nov. 30. (Reporting by David Adams and Jane Sutton; Editing by Philip Barbara)