SOUTH PADRE ISLAND, Texas (CNN) -- Dolly became a Category 1 hurricane Tuesday afternoon in the western Gulf of Mexico, prompting a weather official to urge anyone on Texas' barrier islands to consider leaving immediately.
National Hurricane Center Director Bill Read also said heavy rain and flooding, rather than Dolly's winds, were the forecasters' biggest concern for extreme southern Texas and northeastern Mexico.
Dolly, formerly a tropical storm, was heading toward those areas and was expected to make landfall at about noon Wednesday, forecasters said.
"Anyone in the far South Texas barrier islands who don't want to ride out the rough conditions of a hurricane should be leaving now and not waiting until tomorrow," Read said.
By Wednesday, Read said, it probably will be too late to escape the storm because roads could be "easily overwashed."
At 11 p.m. ET, the storm, with maximum sustained winds near 80 mph, was centered in the Gulf of Mexico about 110 miles east-southeast of Brownsville, Texas, the hurricane center said. See Dolly's projected path »
A Category 1 hurricane carries sustained winds between 74 mph and 95 mph. Dolly was expected to strengthen before landfall, but the hurricane center was predicting it wouldn't be stronger than Category 1, Read said.
A hurricane warning was in effect for the Texas coast from Brownsville to Corpus Christi and for northeast Mexico from Rio San Fernando to the U.S. border. iReport.com: Are you ready for hurricane season?
Dolly is expected to drop generally 6 to 10 inches of rain -- with isolated amounts of 15 inches in some areas -- over much of South Texas and northeastern Mexico, according to the hurricane center.
"Our biggest concern is going to be after the landfall -- the very heavy rain that will occur," Read said.
Radar indicated that the first band of heavy rain would hit the shoreline between Port Isabel, Texas, and Brownsville late Tuesday night, CNN Meteorologist Sean Morris said.
Coastal winds were expected to reach near-hurricane strength by dawn near the Brownsville Ship Channel and Port Isabel, he said. Tornadoes were possible Tuesday night and Wednesday morning across the middle and lower coasts of Texas, according to the hurricane center.
Forecasters said Dolly would move slowly and possibly be only 80 miles inland by Wednesday evening, meaning that torrential rain and battering waves would assault the coastline for most of Wednesday.
Tropical storm warnings were issued for residents living north of Corpus Christi to San Luis Pass, Texas. The region from Rio San Fernando to La Pesca, Mexico, is under a hurricane watch as well as a tropical storm warning.
Because of the approaching storm, more than 1,000 detainees accused of being illegal immigrants were transferred from a facility in Port Isabel, Texas, to other Texas detention facilities, according to Immigration and Customs Enforcement spokeswoman Nina Pruneda.
Texas Gov. Rick Perry activated 1,200 National Guard troops and other emergency crews.
In Mexico, officials were planning to evacuate 23,000 people to government shelters, Tamaulipas Gov. Eugenio Hernandez said, according to The Associated Press.
In Brownsville, residents were boarding windows and placing sandbags on their properties Tuesday, hoping to keep any floodwaters from their homes.
Some people lined up outside a Brownsville school to get up to 20 free bags of sand each. Maribel Vallejo waited two hours, but she said she wasn't complaining.
"I'm being patient because it's something we have to do to avoid any flooding going into our homes," she said.
Brownsville Mayor Pat Ahumada said Tuesday that he didn't foresee a need for mandatory evacuations.
"People can evacuate voluntarily if they want to, but I think we can weather the storm out just by staying vigilant and staying indoors," Ahumada said.
Hotels and businesses in the Texas resort of South Padre Island also were boarding their windows Tuesday, CNN meteorologist Reynolds Wolf reported. Some tourists were cutting their vacations short, he said. Watch people preparing as storm approaches »
Shell Oil told the AP that it was evacuating workers from oil rigs in the western Gulf of Mexico.
More than 100 U.S. Navy aircraft based in Corpus Christi were flown to bases inland because of the storm, the AP reported.
Meanwhile, a number of ships taking part in exercises off the mid-Atlantic coast were repositioned to avoid Tropical Storm Cristobal, a Navy spokesman said.
Early Tuesday, Cristobal paralleled the Atlantic Seaboard as it slowly began losing steam. See Cristobal's projected path »
At 5 p.m. ET, Cristobal was moving toward the northeast near 28 mph, about 170 miles south-southwest of Halifax, Nova Scotia.
The storm was packing 50-mph winds but was expected to weaken over the next 24 hours.
The Atlantic hurricane season began June 1 and runs through November.
CNN's Brian Todd and Barbara Starr contributed to this report.
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