A weakening Tropical Storm Paul swerved away from a landfall on a sparsely populated stretch of Mexico's southern Baja peninsula Tuesday night, brushing the coast with wind and rain as it swirled northward just offshore.

Forecasters said the storm could make a brief sweep across land at midday Wednesday before veering northwestward back into the Pacific.

The storm had been predicted to come ashore farther south Tuesday night and move up the spine of the peninsula, causing authorities to take precautions even as Paul was losing hurricane strength.

Officials in the Gulf of California city of Mulege evacuated families in vulnerable areas or flimsy housing, and army and navy units were on hand for emergencies and disaster relief. Officials in the flood-prone city of Ciudad Constitution opened 26 shelters for local residents, and residents were advised to stay inside and stock up on drinking water.

Rain fell on the small gulfside resort of Loreto, but residents felt protected by the chain of mountains running up the center of the peninsula.

"We don't foresee any big concern," Pascal Pellegrino, the Italian-born manager of the Oasis Hotel, said, adding that there were relatively few tourists in Loreto, perhaps 400 or 500.

Pellegrino said the worst problem that hotel keepers feared was a loss of electrical power.

The National Hurricane Center said Paul's maximum sustained winds had decreased to 60 mph (95 kph) Tuesday night. It was moving north at 12 mph (19 kph).

Rain caused flooding in some neighborhoods of Cabo San Lucas at the southern tip of the peninsula, but the storm mostly passed by the heavily populated tourist area.

As a precaution, the state government suspended school statewide Tuesday, and ports were closed to small vessels in the capital of La Paz, Los Cabos and Comondu.

A tropical storm warning was in effect for the western coast from Santa Fe north to El Pocito and in the east from San Evaristo to Bahia San Juan Bautista.

In the Atlantic, meanwhile, Hurricane Rafael moved rapidly northward to the east of Bermuda late Tuesday, pelting the British territory with rain and wind.