"Further strengthening is likely and Dolly could become a hurricane during the next 24 hours," the U.S. National Hurricane Center said. Maximum sustained winds were 50 mph at 8 a.m. EDT.
The storm was centered about 300 miles east-southeast of Tampico or 450 miles southeast of Brownsville, Texas. It was moving west-northwest at 12 mph.
The storm's track gives hope to farmers in the Texas-Mexico border region who have been looking for rain to alleviate a severe drought in the region.
Dolly briefly reached hurricane force of 74 mph as it smacked the Yucatan Peninsula on Tuesday. Its journey across the peninsula knocked its winds back to about 35 mph a day later.
Cyclonic storms tend to disintegrate when they move over land and pick up strengthen when they hit warm water.
Storm alerts and warnings were in force all along the upper coast of the Gulf of Mexico, including Veracruz and Tamaulipas states. Officials there warned small craft to return to port and prepared shelters for people in low-lying areas who might have to evacuate.
There have been no confirmed deaths, but at least two fishermen were still reported missing. Officials in the Caribbean coastal state of Quintana Roo said 16 houses were destroyed there and 26 others damaged by the storm.
The state oil monopoly, Petroleos Mexicanos, evacuated dozens of its offshore oil and gas wells in Campeche Bay as a precaution.