FEMA Director Rich Serino said two disaster recovery centers opened Wednesday and many more will open in the coming days.
Twenty-nine people stayed overnight in the six Red Cross shelters set up in Moore, but around 150 have cycled in and out throughout the day, said Serino.
Moore Mayer Glenn Lewis said all residents will be allowed back to their neighborhoods by 3 p.m. Wednesday.
Fallin said her office has received multiple phone calls and requests from people interested in donating money for safe rooms. She said she plans to announce something later in the day with regard to a "safe room fund."
Earlier Wednesday, the state medical examiner released the identities for most of the 24 victims, though next-of-kin notifications were still taking place for others. The causes of death were listed as blunt force trauma and asphyxiation.
White House spokesman Jay Carney said the president is scheduled to visit the tornado-ravaged city Sunday and meet with victims and first responders.