Forecasters on Wednesday feared Rita could further intensify in the Gulf and the storm's most likely destination by the end of the week was Texas, although Louisiana and northern Mexico were possibilities.
On the far side of the Gulf of Mexico in Texas, Galveston started evacuations and officials made plans to move survivors from Hurricane Katrina who had been housed in the Houston area to Arkansas.
Acting Federal Emergency Management Agency Director David Paulison said the agency had aircraft and buses available to evacuate residents of areas the hurricane might hit.
Rescue teams and truckloads of ice, water and prepared meals were being sent to Texas and Florida.
"I strongly urge Gulf Coast residents to pay attention" to the storm, he said.
Stung by criticism of the government's slow initial response to Hurricane Katrina, President George Bush signed an emergency declaration for Florida even though it appeared Rita had largely spared the Keys.
"All up and down the coastline people are now preparing for what is anticipated to be another significant storm," Bush said.
Florida services ready
Florida governor Jeb Bush said more than 2000 Florida National Guard troops and dozens of law enforcement officers were ready to deal with the storm's aftermath.
"I think we did, so far, dodge a bullet," said Key West
"There's still plenty of warm water that it needs to move over in the next couple of days. The forecast is favourable for further intensification"
Michelle Mainelli, meteorologist, National Hurricane Centre
mayor Jimmy Weekley.
Rita started the day as a tropical storm with top sustained winds of up to 113kph (70mph). But as it cruised through the Florida Straits between the Keys and Cuba, it gathered energy from the warm sea.
Bush received a briefing about Rita on board the USS Iwo Jima, which is docked near downtown New Orleans, as the hurricane caused new anxiety among Katrina victims in Mississippi, Louisiana and Alabama.
"There's still plenty of warm water that it needs to move over in the next couple of days. The forecast is favourable for further intensification," said Michelle Mainelli, a meteorologist at the National Hurricane Centre.
Residents and visitors had been ordered out of the Keys, and voluntary evacuation orders were posted for coastal mainland areas such as Miami Beach.
About 130,000 people were evacuated in Cuba, on the southern side of the Florida Straits.
The storm churned up roiling waves and soaked the northern coast as it made its way past Havana in the late afternoon.
Electricity, gas and water services were interrupted in neighbourhoods around the capital of 2 million, and some streets were flooded.
Havana's international airport was closed to incoming and outgoing flights.
Many of Key West's shops and bars were boarded up.
"This city was really very well prepared," said Jim Gilleran, owner of the 801 Bar in the Old Town section of Key West.
He kept his business open despite the heavy rain and a power outage.
Tropical storm Rita strengthened
into a hurricane on Tuesday
At least one segment of the Keys highway, US 1, was barricaded because of water and debris, the Florida Highway
Wind-driven water was flowing across other sections of the two- and three-lane highway that connects the Keys.
Rita moving west
At 2am (0600 GMT), Rita's eye was about 233km west of Key West. The storm was moving west at 22.5kph - a track that kept the most destructive winds at sea and away from Key West.
Nearly 1500km from Key West, officials of Galveston were already calling for voluntary evacuations, with mandatory evacuations to begin on Wednesday.
Louisiana governor Kathleen Blanco urged everyone in the southwest part of the state to prepare to evacuate.
Even those who had survived major hurricanes were getting ready to leave.
Catherine Womack, 71, was busy boarding up the windows on her one-story brick house in Galveston.
"Destination unknown," she said. "I've never left before. I think because of Katrina, there is a lot of anxiety and concern. It's better to be safe than sorry."
New Orleans mayor Ray Nagin suspended his plan on Monday to start bringing residents back to the city after warnings that Rita could follow Hurricane Katrina's course and rupture his city's weakened levees.
Rita lashed low-lying islands of
the Florida Keys with rainy squalls
The Pentagon stationed coordinating officers and staff at Tallahassee, Florida, and Austin, Texas, to assist storm preparations and recovery.
The USS Bataan, an amphibious assault ship, was off Florida's Atlantic coast near Jacksonville, preparing to follow behind Rita to support relief efforts.
Oil prices affected
The hurricane lifted crude oil prices more than $1 late on Tuesday in electronic trading on the New York Mercantile Exchange, sending futures back above $67 a barrel as workers fled facilities in the Gulf of Mexico.
Katrina destroyed 46 platforms and rigs and significantly damaged 18 platforms and rigs, according to the American Petroleum Institute.
Rita is the 17th named storm of the Atlantic hurricane season, making this the fourth-busiest season so far since record-keeping started in 1851.
The record is 21 tropical storms in 1933. Six hurricanes have hit Florida in the last 13 months.
The hurricane season is not over until 30 November.