Renamed Hurricane Douglas from Hurricane Cesar because of the move, the storm was about 300 miles southeast of the Mexican resort of Acapulco on Monday evening.
After dissipating during its trip across the isthmus, the storm regrouped in waters considerably warmer than its Caribbean birthplace, the U.S. National Hurricane Center in Miami said. Warmer waters mean more energy for the hurricane.
The Mexican government issued a tropical storm warning from Salina Cruz to Acapulco as Douglas headed west at about 20 miles an hour with sustained winds of 80 mph and gusts of 97 mph.
Up to six inches of rain fell over parts of southern Mexico and in some places tides were expected to be four feet above normal.
Cesar was blamed for 11 deaths in Colombia as it lashed the San Andres archipelago. The toll included eight children who died in an avalanche blamed on Cesar's heavy rains.
The storm barreled across Central America on Sunday, with Nicaragua taking the brunt.
Damage reports from Cesar were slow to come in from outlying areas without telephone and electrical service.
But Costa Rica's government confirmed 11 deaths from heavy flooding in the south. The Costa Rican Red Cross said 10 other people were missing in a mudslide that buried a house in Terrazu, 40 miles south of the capital, San Jose.
"I was outside my house fixing a fence when I heard a roar and felt the ground shake. Then I saw this mountain of earth bury my house and all my family inside," Rigoberto Calderon said.
Swollen rivers jumped their banks Sunday night and left a still-uncounted number of injured and homeless.
"Dozens of homes were washed away, some with entire families inside, so we still don't know how many people were killed," said Carlos Quesada, director of the National Emergency Commission.
Much of the flooding was reported around Perez Zeledon, 70 miles south of the Costa Rican capital.
In neighboring Nicaragua, the government declared an emergency and sent army helicopters with food, medicine and blankets to flooded areas.
At least 10,000 Nicaraguans were left homeless by flooding, authorities said. Two youths drowned and a boy was asphyxiated in the chaos of an evacuation in a crowded truck, officials said.
Schools closed Monday in much of Nicaragua. Health Minister Federico Munoz said outbreaks of cholera and other diseases where feared in some remote areas.
In El Salvador, the storm left dozens homeless and was blamed for at least 10 deaths, most in slides.
No deaths or injuries were reported in Guatemala despite heavy rains.
Even comparatively weak hurricanes and tropical storms wreak heavy damage in impoverished Central America, where most people live in frail homes easily washed away. Hurricane Bertha, with winds over 100 mph, killed at least 10 people earlier this month in the Caribbean and along the U.S. eastern seaboard.
Two hurricanes and one tropical storm have hit Mexico's Pacific coast this storm season.
Copyright =A9 1996 The Associated Press.