The storm dumped up to a foot of rain and lashed the border region of the two states with 120 mile per hour winds when it crashed ashore from the Gulf of Mexico on Saturday.
Rita pushed in a 15-foot storm surge that swamped the Cajun communities of southern Louisiana and left hundreds of people stranded in or on top of their submerged homes.
The storm dealt a glancing blow to Houston, center of the U.S. oil industry, but badly damaged small towns and cities to its east.
Shaken survivors emerged to find a panorama of destroyed buildings, debris-strewn streets, downed power lines and toppled trees. Those who defied evacuation orders and rode out the storm said it was a frightening experience.
"I called on Jesus for four hours," Gloria Matthews told the Beaumont Enterprise. "The house was shaking and the wind was roaring."
A key natural gas installation in southern Louisiana known as Henry Hub, through which a third of the nation's natural gas flows and where spot gas prices are determined, was damaged by Rita, Louisiana Gov. Kathleen Blanco said.
"We understand there is a gas leak and...a possible shearing of an oil storage tank," Blanco told CNN.
She gave no other details about the damage or its effects on gas delivery, but said the leak would have to be plugged.
"We're watching the situation very carefully," Blanco said.
Rita and Katrina knocked out nearly all energy production in the offshore oil fields of the Gulf of Mexico and 30 percent of the U.S. refining capacity onshore.
At least three oil refineries were damaged by Rita, oil companies said.
Rita cut power to more than 2 million people in Texas and Louisiana. Utility companies said it could take a month to fully restore electricity in the stricken region.
Risk modeling experts said up to $6 billion in damages had been inflicted by Rita, which came less than a month after Hurricane Katrina struck Mississippi and Louisiana, leaving the historic city of New Orleans in ruins.
"We have been struck with another very strong hurricane and south Louisiana has been dealt a harsh blow, in fact all of Louisiana has been dealt a harsh blow," said Blanco, who toured the damage from Rita on Saturday.
More than a 1,000 people died from Katrina, but there was only one known Rita-relate death--a person killed by a tornado in Belzoni, Miss.
In scenes similar to those that followed Katrina, emergency workers in boats and helicopters went to flooded areas to save people who had not fled Rita and found themselves stranded in waters up to nine feet deep.
In towns such as Abbeville, Pecan Island and Dulac, where French-speaking Cajuns settled and the Cajun culture is still strong, rescue workers battled high winds that continued to push water inland to pluck people from roofs or carry them from their homes.
"We need to pray to the good lord to switch the wind's direction," said Vermilion Parish Sheriff Mike Couvillan.
Rita's storm surge was so powerful that Couvillan said it reached his own ranch 35 miles inland.
Unlike New Orleans and Katrina, rescue workers arrived quickly after the storm and there was no repeat of the shocking scenes of crime and chaos that besieged the Big Easy.
In Texas, chaos preceded Rita in a different form as nearly 3 million people fled the coast to escape what was once a dangerous Category 5 storm with 175 mile per hour winds.
The mass evacuation caused 100-mile-long traffic jams and depleted gasoline supplies in the Houston area. Cars that overheated or ran out of gas lined the state's highways.
A bus carrying elderly people from a Houston nursing home exploded, killing 23 of those on board.
On Saturday, Texas officials desperate to avoid new traffic jams as evacuees go home, urged people to delay their return. They announced a voluntary plan in which evacuees would come back over the next three days, depending on where they live.
"I can't say in strong enough terms to those who evacuated the coastal region that they should not begin their return for the time being," Gov. Rick Perry said.
He also encouraged oil companies to refuel gas stations to assure an adequate supply of gasoline.
Despite Perry's pleas, evacuees began flooding back to Houston on Saturday, causing backups on some highways.
Gasoline was still in such short supply that the few gas stations open had long lines of cars waiting to fill their tanks.
The center of Rita came ashore 200 miles west of New Orleans, but its storm surge caused new flooding in the city that was just drying out from Katrina.
The U.S. Army Corps of Engineers worked to plug levees fractured by Katrina and now swamped again by Rita, but parts of New Orleans, now largely deserted, were again covered by up to 12 feet of water.
Still, Mayor Ray Nagin said he would move ahead with a plan to repopulate the least-damaged parts of the city by Katrina and Rita by allowing residents of the Algiers section back in as early as Monday.
"We want to bring New Orleans back," he said.
Weather forecasters said on Sunday Rita had diminished to a tropical depression with heavy rains and sustained winds of 20 mph. It was located near Hot Springs, Arkansas and moving northeast at 20 mph.