The biggest search and rescue operation in Texas history was set to continue Monday and thousands of people faced long stays in crowded shelters because their homes were damaged or destroyed by Hurricane Ike.

The death toll from Ike rose to 30 in eight states, many of them far to the north of the Gulf Coast as the storm slogged across the nation’s midsection, leaving a trail of flooding and destruction. Glass-strewn Houston was placed under a weeklong curfew, and millions of people in the storm’s path remained in the dark.

Rescuers said they had saved nearly 2,000 people from waterlogged streets and splintered houses by Sunday afternoon. Many had ignored evacuation orders and tried to ride out the storm. Now they were boarding buses for indefinite stays at shelters in San Antonio and Austin.

‘‘I have nowhere to go,’’ said Ldyyan Jonjocque, 61, waiting for a bus while holding the leashes of her four Australian shepherd dogs. She said she had to leave two dogs behind in her home. She wept as she told of officers rescuing her in a dump truck.

In hard-hit towns like Orange, Bridge City and Galveston, authorities continued their door-to-door search well into the night, hoping to reach an untold number of people still in their homes, many without power or supplies.

Many of those who did make it to safety boarded buses without knowing where they were going or when they could return to what might remain of their homes.

Shelters across Texas scurried to find enough cots, and some evacuees arrived with little cash and no idea of what the coming days held.

Even for those who still have a home to go to, Ike’s 110 mph winds and battering waves left thousands in coastal areas without electricity, gas and basic communications — and officials estimated it may not be restored for a month.

‘‘We want our citizens to stay where they are,’’ said a weary Galveston Mayor Lyda Ann Thomas. ‘‘Do not come back to Galveston. You cannot live here at this time.’’

Michael Geml has braved other storms in his bayfront neighborhood in Galveston, where he’s lived for 25 years, though none quite like Ike. The 51-year-old stayed in the third-story Jacuzzi of a neighbor’s house, directly on the bay, with family pets as waves crashed across the landscape. But amid the havoc, Geml asked anyone who would listen — even his rescuers — for an odd commodity: cat litter for his spooked feline.

‘‘I’ll never stay again,’’ Geml said. ‘‘I don’t care what the weatherman says — a Category 1, a Category 2. I thought I was going to die.’’

Kathi and Paul Norton huddled inside their house in Crystal Beach until it collapsed and was swept away. Their flag pole kept the house from collapsing on top of them, buying them a few seconds to escape, holding onto the staircase.

‘‘You never know what a hurricane is like until you ride it on a staircase,’’ said Kathi Norton, 47. As she spoke outside the giant, warehouse-like shelter on a former Air Force base in San Antonio, busloads of new evacuees were arriving, bumper to bumper.

The hurricane also battered the heart of the U.S. oil industry as Ike destroyed at least 10 production platforms, officials said. Details about the size and production capacity of the destroyed platforms were not immediately available, but the damage was to only a fraction of the 3,800 platforms in the Gulf.

It was too soon to know how seriously it would affect oil and gas prices.

President Bush made plans to visit the area on Tuesday.

He said getting power restored is an extremely high priority and urged power companies to ‘‘please recruit out-of-state people to come and help you do this.’’

Ike was downgraded to a tropical depression as it moved north. Roads were closed in Kentucky because of high winds. As far north as Chicago, dozens of people in a suburb had to be evacuated by boat. Two million people were without power in Texas, Arkansas and Louisiana.

Of the 30 dead, five were in the hard-hit barrier island city of Galveston, including one body found in a vehicle submerged in floodwater at the airport. There were two other deaths in Texas and six in Louisiana, including a 16-year-old boy trapped in rising floodwaters. Several were farther inland.

Two golfers died when a tree fell on them in Tennessee. There were six deaths in Indiana; three died in Missouri. One person died in Arkansas and three in Ohio, including two motorcyclists killed when a tree toppled on them at a state park.

Ike killed more than 80 in the Caribbean before reaching the U.S.

Houston, the nation’s fourth-largest city, was reduced to near-paralysis in some places. But power was on in downtown office towers Sunday afternoon, and Texas Medical Center, the world’s largest medical complex, was unscathed and remained open. Both places have underground power lines.

Its two airports — including George Bush Intercontinental, one of the busiest in the United States — were set to reopen Monday with limited service. But schools were closed until further notice, and the business district was shuttered.

Five people were arrested at a pawn shop north of Houston and charged with burglary in what Harris County Sheriff’s spokesman Capt. John Martin described as looting, but there was no widespread spike in crime.

Authorities said Sunday afternoon that 1,984 people had been rescued, including 394 by air. Besides people literally plucked to safety, that figure includes people met by crews as they waded through floodwaters trying to find dry ground.

Still others chose to remain in their homes along the Texas coast even after the danger of the storm had passed. There was no immediate count Sunday of how many people remained in their homes, or how many were in danger. The Red Cross reported 42,000 people were at state and Red Cross shelters Saturday night.

The search-and-rescue effort included more than 50 helicopters, and 1,500 searchers and teams from federal, state and local agencies.

From the city of Orange alone, near the Louisiana line, more than 700 people sought dry ground — ‘‘a Herculean effort to organize a reverse evacuation that nobody had ever planned for,’’ Mayor Brown Claybar said.

Rescue crews vowed to continue the search until they had knocked on every door. They were helped by receding floodwaters, but there were constant surprises as people rowed and sloshed through towns.

The storm also took a toll in Louisiana, where hundreds of homes were flooded and power outages worsened as the state struggles to recover from Hurricane Gustav, which struck over Labor Day.

In Hackberry, La., about 15 miles from the coast, workers moved a large shrimp boat out of the highway with a bulldozer, but the team had to stop because of strong currents in the floodwaters and difficulty in seeing the roadway.

Thayne Culbertson, a disabled veteran and commercial fisherman, rode out the storm at a friend’s apartment in Galveston. As someone who has been through several hurricanes, he decided to stay behind for Ike in case he could help.

Instead, help had to find him. He was picked up by a helicopter after a toppled utility pole battered the building and windows were blown out. He later boarded a bus to San Antonio.

During the storm, he said, ‘‘the sand felt like it was peeling away your skin.’’