Inspectors with the corps and the city's Public Works and Engineering Department were on the scene Thursday of the nighttime collapse.
Neighbors said they had complained to apartment managers about cracks in the staircases.
But recent complaints filed against the apartment complex indicated no structural problems, officials said. Public works had inspected the complex for some electrical, plumbing, sanitary and sewer problems, but "nothing that raises any red flags," said department spokesman Alvin Wright.
Neighborhood Protection Corps had received seven complaints since 2004 about the complex but all were minor, covering a lack of air conditioning, or hot water, or the presence of mice, Silva said.
"This one had all minor complaints, a minimal number and every time management had complied," Silva said.
Authorities identified the dead children as Miguel Robledo, 5, and David Vasquez, 10. Autopsies were scheduled for Thursday.
A third boy, 9 years old, was taken to Texas Children's Hospital, apparently with a broken leg. No update on the injured boy's condition was immediately available. The boys were not related.
Houston fire officials said Robledo and Vasquez were playing hide-and-seek in the stairwell and died in the accident that occurred about 7:40 p.m. Wednesday at the Westwood Fountains apartment complex.
Jaime Cuevar helped free the 9-year-old from the fallen concrete. Unstable walls after the collapse delayed firefighters from retrieving the children's bodies from the apartment complex for several hours.
"What they needed to do was to knock down the walls surrounding the stairwells to make it safe for the firefighters to recover the bodies," police spokesman John Cannon said. A large backhoe recovered the bodies around midnight Wednesday, he said.
Some residents were evacuated after the accident and may not be able to return to their apartments until Thursday night, until inspectors are satisfied the building is structurally sound, Wright said.
"The walls are still crumbling out there," he said.
The complex, built in 1979, has 293 apartments, according to county records.
Cannon said apartment complex personnel apparently were going to erect some temporary fencing at the facility.
A call to management at the apartment complex was not immediately returned Thursday.