MEXICO CITY (REUTERS) - Tropical storm Barbara weakened to a depression as it crossed southern Mexico on Thursday headed toward the Gulf of Mexico, with warnings lifted as wind speeds dropped, the United States (US) National Hurricane Center said.

Barbara reached hurricane strength on Wednesday, hitting the southern Pacific coast near Mexico's biggest oil refinery and flooding roads, toppling trees and killing three men. It then weakened to a tropical storm as it moved inland.

The depression was near Mexico's Gulf coast, but was described as "very ill-defined" and the threat of heavy rains and flooding continued.

The Red Cross said the Salina Cruz refinery was operating normally. State oil monopoly Pemex said the same on Wednesday but was not immediately available for comment on Thursday.

The depression was located around 64km north-west of the port city of Coatzacoalcos in southern Mexico, with maximum sustained winds dropping to around 48kph, the centre said.

It was moving north-west at 5km/h and was expected to turn toward the west and north-west and move near or along the Gulf coast, the centre added.

"The centre of Barbara is expected to emerge over the extreme south-western Gulf of Mexico later today. Barbara is expected to weaken to a remnant low later today," it said.

Fourteen fishermen were missing in the state of Oaxaca during the storm, local media reported in Mexico. Local emergency services said they could not confirm that information.