Tropical storm Ernesto neared the Mexican port of Coatzacoalcos on Thursday, staying just out to sea as US forecasters warned of torrential rain.
At 1800 GMT, Ernesto was a mere 10km north of the city of some 200 000 people, packing winds of up to 95km per hour, the Miami-based US National Hurricane Centre said.
"Torrential rain and flooding (is) anticipated as Ernesto skirts the coast of Mexico near Coatzacoalcos," it added.
Laura Gurza, the head of Mexico's civil defense agency, appealed to residents in the affected areas to "be aware and respond to instructions from authorities".
Speaking to Milenio Television, she said officials were most concerned about swollen rivers and streams in the state of Veracruz, as well as mountainous areas that are prone to landslides.
The country's state-owned Pemex oil company meanwhile said safety measures had been reinforced at more than 200 offshore oil platforms in the Gulf of Mexico.
A tropical storm warning was in effect from the port of Veracruz to Chilitepec as forecasters said Ernesto was expected to move over southern Mexico later on Thursday and Friday and weaken within the next 48 hours.
Through Friday, Ernesto was expected to dump up to 25cm of rain on the Mexican states of Veracruz, Tabasco, Puebla and Oaxaca. Some parts of Veracruz could see as much as 38cm.
"These rains may produce life-threatening flash floods and mud slides over areas of higher terrain," the NHC said, adding that the surge will be accompanied by "large and dangerous" waves along the coast.
The storm, which initially came ashore on the Yucatan Peninsula Tuesday as a category one hurricane before being downgraded to a tropical storm, caused some damage to the airport of Chetumal, a city of 151 000.
In Majahual, a small town with a growing tourism industry in Mexico's Quintana Roo state, businesses suffered some damage.
Power outages were reported in the walled city of Campeche, a world heritage site on the west coast of the Yucatan Peninsula.
The storm — which was the second hurricane of the Atlantic season — began drenching Caribbean countries last week and also dumped heavy rains on areas of Belize, Guatemala and Honduras.
In the Pacific, Gilma strengthened into a hurricane late Wednesday — a category one storm on the five-point Saffir-Simpson wind speed scale.
At 0900 GMT Thursday, it was located about 1175km southwest of the southern tip of Baja California, and was not expected to pose a threat to land.
Also Thursday, the National Oceanic and Atmospheric Administration raised its prediction for the current hurricane season, which runs from 1 June to 30 November.
The latest outlook calls for 12 to 17 named storms, including five to eight hurricanes of which two to three could be major.
In May, it had forecast nine to 15 named storms, including four to eight hurricanes of which it said one to three could be major.
"We are increasing the likelihood of an above-normal season because storm-conducive wind patterns and warmer-than-normal sea surface temperatures" in the Atlantic, said Gerry Bell, lead seasonal hurricane forecaster.