"It's raining intermittently, it rains, its stops, and then it rains again," said Juventino Martinez, the city's civil defense chief. "We have some flooding, some water building up" on streets in lower-lying sections of the city. He said 40 shelters were ready but hadn't been used yet.
Municipal employee Brito Gomez reported water was waist-high in some neighborhoods.
About 2,000 army and navy personnel are on stand-by to head to the jungle-clad hillside inland to help in rescue work if needed, said Noemi Guzman, Veracruz state civil defense director. Guzman said no flooding had yet been reported at any of the state's many rivers.
The U.S. National Hurricane Center said the storm's sustained winds had declined to about 60 mph at midday Thursday as it interacted with land along the coast. It had grown into a hurricane shortly before landfall Tuesday night near the cruise ship port of Mahahual, but it weakened as it crossed the peninsula. Ernesto then steamed back out in the Gulf of Mexico.
Forecasters said Ernesto was expected to roar through Veracruz state's lush Los Tuxtlas region, roughly 50 miles northwest of Coatzacoalcos, creating the threat of torrential flooding.
Much of the storm was already over land Thursday morning and it was centered about 5 miles north of Coatzacoalcos, moving to the west at 5 mph.
The hurricane center said Ernesto was expected to produce rainfalls of up to 15 inches in some parts of the mountainous areas of Veracruz, Tabasco Puebla and Oaxaca.
With many small communities clinging to hillsides in those states, authorities are worried about potential flash floods and mudslides.
Petroleos Mexicanos, the state oil monopoly, announced it had evacuated 61 workers from a drilling platform and had taken other safety precautions, but it said production had not been affected.
There were no reports of storm deaths or major damage, though Ernesto ripped down billboards, toppled trees and cut electricity as it hit land well south of the region's main resorts of Cancun and the Riviera Maya and then passed near the Mayan ruins of Calakmul.
In the Pacific, Hurricane Gilma gained some strength but was not seen as a threat to land. Early Thursday, it was about 730 miles southwest of the southern tip of Mexico's Baja California Peninsula, with maximum sustained winds near 80 mph.