The tropical storm warning was in effect along Mexico's Gulf Coast from Veracruz to Ciudad del Carmen, the National Meteorological Service spokesman Juan Jose Pastrana said.
"Larry" has dumped heavy rains for days and made landfall in the state of Tabasco, Pastrana said.
The storm is packing sustained winds of 95 kilometers (60 miles) per hour with gusts up to 110 kilometers (70 miles) per hour, Pastrana said.
At 1800 GMT, Larry was centered at 18.2 degrees north latitude and 93.6 west, or 90 kilometers (55 miles) east of Coatzacoalcos.
The National Hurricane Center expects Larry to weaken and become a tropical depression later Sunday. It is drifting erratically but moving generally southward.
The center also said storm surges one to three feet above normal would cause flooding. The storm was expected to drop a total of eight to 12 inches of rain and even more in some areas.
Mexico's Civil Defense Service declared a state of emergency in certain municipalities of the states of Tabasco and in the states of Veracruz, Campeche, Yucatan and in Chiapas, which borders on Guatemala.
Campeche, Chiapas, Tabasco and Veracruz set up 75 shelters for some 1,500 people who had been forced from their homes, Civil Defense coordinator Carmen Segura said.
The states of Oaxaca, Guerrero, Michoacan and Colima have also been warned that tropical storm "Olaf" is bearing down on them from the Pacific Ocean.
At 1330 GMT, Olaf was 225 kilometers (140 miles) west-southwest of the city of Lazaro Cardenas, Michoacan. It was headed north with winds of 100 kilometers (60 miles) an hour with gusts of 120 kilometers (75 miles) per hour, the service said.
Ships have been ordered out of the area. Many tourist resorts have been closed because of heavy rains.
Hurricane "Nora" is a level two storm headed north-northwest toward the Pacific Coast of Baja California, where it has caused moderate rains. At 1330 GMT, it was 560 kilometers (350 miles) southwest of Cape San Lucas, Baja California, with winds of 160 kilometers (100 miles) per hour with gusts of up to 195 kilometers (120 miles) per hour.
In recent weeks more than 50 people have died from the heavy storm season in Mexico.