The weather service said it sent four teams to survey damage along the path of the tornado, which traveled 17 miles during a 40-minute period, leaving at least 24 people dead. At its maximum, it was 1.3 miles wide with winds topping 200 mph.
Damage experts said the storm intensified from EF-0 to EF-4 within the first 10 minutes and damage to some areas was determined to have been caused when it reached the EF-5 level.
U.S. President Barack Obama, who signed a disaster declaration Monday night, pledged the victims of the tornado would get "everything they need" as quickly as possible to recover.
Disaster workers crawled across piles of debris Tuesday in hopes of finding survivors.
"It's been a very trying couple of days," Fallin told a news conference, noting damage also was caused by tornadoes that ripped through the state Sunday. "We will get through this."
Fallin thanked first responders and federal emergency management officials for their efforts.
"It's been a heartbreaking experience, especially the loss of children," she said, noting it was unclear whether anyone else was missing. Fallin pledged "every piece of debris, every building" will be examined to see if someone survived.
Fallin said she flew along the path of the twister.
"It was hard to look at, so much debris," she said, adding that in many areas all that was left were bricks and sticks.
"You can't tell where the streets were," she said.
FEMA Administrator Craig Fugate pledged the search for survivors would continue until everyone was found. He urged those who had fled the area without letting anyone know to get in contact with officials.
"In an instant, neighborhoods were destroyed, dozens of people lost their lives, many more were injured," Obama said in Washington. "And among the victims were young children trying to take shelter in the safest place they knew, their school."
"Our prayers are with people of Oklahoma today," he said, praising teachers "who gave their all who gave their all to shield their children," neighbors, first responders and emergency personnel who raced to help as soon as the tornado passed.
"[Our] full focus right now is on the urgent work of rescue and the hard work of recovery and rebuilding that lies ahead," he said.
He said he spoke with Fallin and Moore Mayor Glenn Lewis to assure them they would have the resources they need.
"So the people of Moore should know that their country will remain on the ground there for them, beside them as long as it takes for their homes and schools to rebuild, businesses and hospitals to reopen, their parents to console, first responders to comfort, and, of course, frightened children who will need our continued love and attention," Obama said. "There are empty spaces where there used to be living rooms and bedrooms, and classrooms, and in time we're going to need to refill those spaces with love and laughter and community."
"In some cases there will be enormous grief that has to be absorbed, but you will not travel that path alone. Your country will travel with you," Obama said.
In a media availability, House Speaker John Boehner, R-Ohio, pledged to work with administration officials to make sure "they have the resources they need to help the people of Oklahoma."
Confronted by a question about the lack of support for providing aid in the aftermath of Hurricane Sandy in October -- some conservative Republicans indicated they were considering budget offsets as a condition to the aid that wasn't approved until January -- Boehner said, "Well, listen, let me just speak on behalf of all of our members, including those from Oklahoma, that we will work with the administration to make sure that they have the resources they need."
Amy Elliott, a spokeswoman for the Oklahoma City medical examiner, said an earlier count of at least 51 dead and another 40 bodies in need of processing was no longer accurate, The New York Times reported. Elliott said the medical examiner confirmed 24 deaths. Hospitals reported at least 145 people were injured, 70 of them children.
Firefighters, police, National Guard members and volunteers worked by flashlight overnight and into Tuesday morning looking for victims of Monday afternoon's disaster, CNN reported.
Members of the Air National Guard moved in thermal imaging equipment to aid in the search.
Besides leveling numerous homes and buildings, the tornado destroyed two elementary schools. A third school collapsed but all students were accounted for.
The tornado touched down at 2:56 p.m., 16 minutes after the first warning was issued.
The tornado first struck the town of Newcastle, about 20 miles south of Oklahoma City, and traveled about 10 miles to Moore.
It was the second day of severe weather in the state. A tornado touched down Sunday in Shawnee, 35 miles southeast of Oklahoma City, killing two men and injuring dozens.