Weather forecasters in the US have warned that a tropical storm could gain near-hurricane strength winds before reaching Texas or Louisiana.
The National Hurricane Center (NHC) said Tropical Storm Edouard was crossing the Gulf of Mexico and could make landfall by Tuesday morning.
The governor of Louisiana declared a state of emergency as winds reached sustained speeds of 45mph (75 km/h).
Oil workers have left some offshore rigs but no damage has been reported.
Evacuations
A hurricane watch is in place from west of Intracoastal City, in western Louisiana, to Port O'Connor in Texas, south-west of Galveston.
About 6,000 residents of two communities in western Louisiana had been asked to evacuate low-lying coastal areas.
The mayor of Galveston has not ordered an evacuation but has asked residents and visitors to be prepared.
A storm is considered to be a hurricane once its winds reach an average speed of at least 74mph (119 km/h), according to the NHC.
The Louisiana Offshore Oil Port has stopped offloading tankers and two oil firms were evacuating workers from platforms, Reuters news agency said.
Chevron and Royal Dutch Shell said they were removing employees from rigs as a precaution, but both insisted that production had not been affected.
Oil prices dropped below $120 a barrel on Monday for the first time since early May as it appeared unlikely that the storm would significantly affect oil and gas facilities.
The Houston Ship Channel has also closed.
Hurricane Dolly
At 1300 CDT (1900 BST) Edouard was 145 miles (230km) south-southeast of Lafayette, Louisiana and 240 miles (390km) east-southeast of Galveston, Texas, a statement by the NHC said.
"Edouard could be nearing hurricane strength before reaching the coastline," it added.
Rainfall of 3ins to 5ins (7.6cm to (12.7cm) was predicted in Louisiana, and up to 10 inches (25.4cm) in Texas.
With winds extending outwards from the centre of a tropical storm for 35 miles (56km), residents were braced for the second bout of severe weather to batter the Gulf's coastline in a month.
On 24 July, a state of disaster was declared in 14 Texas counties when Hurricane Dolly lashed the state's coast with winds of 100mph (161km/h).
The Gulf of Mexico supplies about 25% of the US's crude oil.
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