AMBERGIS CAYE, Belize — Tropical Storm Arthur weakened to a tropical depression yesterday after soaking the Yucatan Peninsula, but still threatened to cause dangerous flooding and mudslides in Mexico, Belize, and Guatemala.

The National Hurricane Center in Miami reported that the governments of Belize and Mexico discontinued all warnings related to Arthur, the first named storm of the 2008 Atlantic Hurricane Season.

At about 11 a.m. EDT, the center of the storm was located inland about 125 miles south of Campeche, Mexico. It had maximum sustained winds near 35 mph and was moving west-southwest at about 8 mph.

Forecasters predicted it would remain inland over Mexico and stay well away from the American Gulf Coast.

The hurricane center said Arthur could rain as much as 5 to 10 inches across portions of Belize, Guatemala, and southeastern Mexico, with isolated amounts up to 15 inches possible. It warned of potential life-threatening floods and mudslides.

Arthur formed Saturday afternoon — one day before the official start of the season June 1 — and quickly made landfall at the Belize-Mexico border before heading west.

It dumped rain as far south as Belize City and kicked up strong surf on the popular tourist island of Ambergis Caye, ruining some travelers’ vacations.

“I just came to lay in the sun and get a nice tan, but so far there hasn’t been any sunshine,” said Debbie Fountaineau, a police officer from Lake Charles, Louisiana, who arrived on the island Thursday.