(CNN) -- With everyone missing now accounted for from this week's deadly tornado, the long and difficult work of recovery can begin.
"We are beginning the recovery operations," Oklahoma Gov. Mary Fallin told CNN's Piers Morgan late Wednesday.
"There's a lot of debris removal going on throughout the public areas of the street," she said.
"You see a lot of utility crews that are out here. There's a lot of construction trucks. You're seeing people walking down the street pulling some wagons, going back into their homes to get their prized possessions."
At least 24 people, including 10 children, were killed in Monday's monster tornado. Another 353 people were injured.
The twister ripped through 17 miles of central Oklahoma and pummeled 2,400 homes. The hardest-hit city was Moore.
Moore Mayor Glenn Lewis told CNN's Jake Tapper, also Wednesday, that six people previously unaccounted for have been located.
Five were found alive. The sixth is dead, and the body was located at the medical examiner's office. The mayor was not sure whether that death was included in the official count of 24.
He also told CNN that he would push for a law requiring storm shelters or safe rooms in new homes.
"What we will do is get the stakeholders here in the city ... and we'll discuss what we think we need to have," he said.
"Anybody that lives in any tornado area should have (a storm shelter), but it's just the matter of cost."
Young lives remembered
One of the most heartbreaking scenes in Moore is a pile of wreckage where Plaza Towers Elementary School once stood.
Seven of the 10 children killed in the storm were inside the school when it collapsed.
The children were in a classroom, Moore Fire Chief Gary Bird told CNN on Wednesday. He also said their deaths "had nothing to do with flooding, from what I understand." On Tuesday, Lt. Gov. Todd Lamb told CNN the youngsters had drowned in a school basement.
Local resident Adam Baker said he rushed to the school to help in the aftermath. He found some children who had died in a shallow space.
"The ones that were deceased had bumps, scrapes, and they probably would have made it if they weren't pinned. It looked like most of them just drowned -- all blue and stuff." Pieces of pipe, metal, desks, 2-by-4s, and other debris were on them, he said.
Officials have not yet released official causes of death.
Kyle Davis, 8, was among the victims.
His family said he loved going with his grandpa to see Monster Trucks and playing soccer.
"I am angry to an extent. I know the schools did what they thought they could do but with us living in Oklahoma, tornado shelters should be in every school," Kyle's mother, Mikki Dixon Davis, told CNN.
Her daughter, who was also at Plaza Towers when the storm struck, survived.
"There should be a place that if this ever happened again during school that kids can get to a safe place," she said. "That we don't have to sit there and go through rubble ... and may not ever find what we're looking for."
'We're going to help them recover'
Damage assessments showed the tornado had winds over 200 mph at times, making it an EF5 -- the strongest category of tornadoes measured, the National Weather Service said.
Mayor Lewis said the devastation was so catastrophic that city officials rushed to print new street signs to help guide rescuers and residents through the newly mangled and unfamiliar landscape.
President Obama will travel to the area Sunday to witness the damage.
He spoke about the people of Oklahoma, briefly, during a presentation at the White House on Wednesday.
"While the road ahead will be long, their country will be with them every single step of the way. That's who we are, and that's how we treat our family and friends and our neighbors wherever they are in the country," he said.
"We're going to help them recover."
Insurance claims related to Monday's tornado and storm in metropolitan Oklahoma City are likely to top $2 billion, said Kelly Collins, a representative of the Oklahoma Insurance Department.
Craig Fugate, the Federal Emergency Management Agency administrator, told CNN the agency is in "good shape" to support the recovery in Oklahoma and in other disaster zones, such as rebuilding after Hurricane Sandy in New Jersey and New York.
"We got full allocation last year with the Sandy supplemental funds. We are looking to continue the response here as well as the previous disasters."
But "if we have another hurricane, we may need more money," he said Wednesday.
For her part, Secretary of Homeland Security Janet Napolitano traveled to Moore to thank first responders and show her support.
"Our commitment is to be here for the duration -- to work with our federal, state, tribal, local and community partners in the coming days, weeks and months to help you recover and rebuild from this terrible tragedy and emerge even stronger," she said.
Those helping in Moore include police and firefighters from Joplin, Missouri -- a city all too familiar with grief and devastation.
Wednesday marks the second anniversary of a tornado that pulverized Joplin, killing at least 158 people. It was the deadliest single U.S. tornado since federal record-keeping began in 1950.
"We remember the amount of assistance that we received following the tornado two years ago, and we want to help others as they helped us," said Joplin City Manager Mark Rohr.
"We know too well what their community is facing, and we feel an obligation to serve them as they have served us."
'We just didn't get there fast enough'
Help came from seemingly everywhere the day the tornado struck.
Dustin Ellison ran to the rubble of a convenience store to help get at people trapped in a freezer, which had collapsed.
"It was one big pile of rubble. We knew people had went in the freezer, and we knew that there was no way they had come out," he told CNN's Tapper.
"We just didn't get there fast enough."
One of the victims Ellison and the others found there was 29-year-old Megan Futrell. Another was her infant son, Case.
"She was protecting him," he said.
"Your instinct, when you see that is, for me, I ran towards it. There's probably a lot of people that didn't, or that wouldn't, but not around here."
CNN's Chelsea J. Carter, Kyung Lah, Sara Weisfeldt, Nick Valenica, Brian Todd, Mayra Cuevas, Anderson Cooper, Gary Tuchman, Ed Lavandera, Pamela Brown and George Howell contributed to this report.