Tropical Storm Nate, already dumping rain on Mexico's Gulf coast, was forecast to come ashore midday on Sunday but was not likely to strengthen into a hurricane.
Nate weakened slightly overnight, the Miami-based U.S. National Hurricane Center said.
"Nate is running out of time to strengthen and it appears highly unlikely that it will reach hurricane strength before landfall, which is expected to occur around midday," the hurricane center said in its 5 a.m. ET (0900 GMT) advisory.
The storm had maximum sustained winds of near 60 mph (95 kph) with higher gusts, and little change in strength was expected before landfall, the center added.
The oil-exporting ports of Cayo Arcas and Dos Bocas remained closed to shipping and two other smaller ports were also shut in the southwest Gulf of Mexico.
Strong waves and wind gusts forced beach restaurant owners to pick up chairs and tables and fold umbrellas to prevent accidents.
People in the city of Tuxpan, in northern Veracruz state on the Gulf of Mexico, carried on with business as usual on Saturday, with families gathering at cafeterias and shopping at grocery stores.
Mexico's government has replaced a hurricane warning from Tuxpan to Veracruz with a tropical storm warning, the hurricane center said.
State oil company Pemex evacuated 473 workers from five sea platforms as a precaution. Nate had cut Mexican oil production by 178,800 barrels a day as of Friday.
Local media reported a fisherman drowned on Friday after strong surf capsized his little boat in the Bay of Campeche area, and 10 oil industry contractors were missing after they evacuated a rig in the same area.
To the east, Caribbean islands that were lashed by Hurricane Irene last month looked set to be spared any major impact from Tropical Storm Maria.
Maria, with maximum sustained increasing to near 60 mph (95 kph), was moving toward the northwest.
"The center of Maria will move gradually away from the extreme northeastern Caribbean islands and move over the open Atlantic," the National Hurricane Center said.
"No significant change in strength is anticipated during the next two days," the center added.
ReutersLast Mod: 11 Eylül 2011, 12:45