Earlier, mainland residents were urged to move away from levees in case they were breached.
But shortly before its centre came ashore, the storm veered north and away from the flood walls.
"The levees are holding up just fine, there is no indication right now that they are going to crest," Johnny Cavazos, emergency co-ordinator for Cameron County, said.
Based on Dolly's projected path, the US Census Bureau said that about 1.5 million Texans could feel the storm's effects.
Cari Lambrecht, a spokesman for Hidalgo County, Texas, said people in low-lying areas were being encouraged to use public shelters.
"It's so much easier for them to go now instead of us having to pull them out later," she said.
In Mexico, Governor Eugenio Hernandez of the state of Tamaulipas, said 50 neighbourhoods were still in danger from flooding and about 13,000 people had taken refuge in government shelters.
"Strong winds are no longer the problem. Now we have to worry about intense rain in the next 24 hours," Mr Hernandez said.
Officials in the Mexican city of Matamoros told the AFP news agency that high winds brought by Dolly had damaged the main water treatment plant, leaving some 250,000 people without drinking water, while rains had caused widespread flooding.
In the Gulf of Mexico, Shell Oil evacuated workers from oil rigs, but said it did not expect production to be affected.
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