Capt. D.W. Ready said the shooter was dressed in some kind of military uniform and had Nazi emblems with him and at his house.
However, Ready would not speculate on whether the Nazi insignia would help establish a motive. He said the emblems may have been collector's items. At the shooter's home, police found vintage military equipment and paraphernalia dating back to the Civil War.
"At this point we are very open-minded as to the motive," said acting Chief Martha Montalvo.
She described the shooter as a lawyer who had "issues" at his law office.
Gunshots brought quick police response
The Bellaire Police Department and West University Police Department also responded with Houston police to the report of an active shooter in a neighborhood strip mall in the affluent neighborhood of West University Place at 6:30 a.m.
Nine officers engaged the gunman in a gunfight while assisting wounded citizens, Ready said. The gunman took cover behind a tree, he said.
"Multiple officers engaged the suspect, who was shooting randomly at passersby as well as anybody he could put his sights on," Ready said. "He was wearing a military-style apparel, I don't know exactly what nationality or exactly what army or anything like that."
More than 75 expended shell casings were found at the scene, and the gunman had 2,600 rounds of ammunition for his .45-caliber pistol and .45-caliber Thompson carbine rifle, which carried a 40-round clip, Ready said.
Attorney Nathan DeSai has been identified as the shooter, Houston Mayor Sylvester Turner said. Police declined to identify the gunman publicly.
DeSai was a lone gunman who was disgruntled over matters at the law firm where he worked, according to the mayor, who said he'd been briefed on the shooting by police. DeSai practiced business, criminal and family law, according to his profile on the State Bar of Texas website
Police said one victim was critically wounded and another was seriously wounded. The rifle was purchased legally in 2009, and the handgun was purchased legally in 2011, Montalvo said.
Witness: Gunshots flew by my face
It was still dark when Antoine Wilson drove through the neighborhood Monday morning and suddenly found himself in the middle of a gunfight.
"I didn't realize I was right there by the shooter," he told CNN affiliate KTRK
. "Gunshots, I literally hear the gunshots pass my face, 'cause I'm leaning out the window looking, trying to see."
Then he saw police running down the street.
"You (could) hear people screaming," he said. "I'm talking about steady gunshots, just steady shooting, back and forth ... police and the shooter. Helicopters were everywhere."
Firefighters and police swarmed the scene as gunfire rang out, KTRK reported.
"I'm still shaken up," Wilson told KTRK. "I've never been in no standoff like this before."
Later Monday, Kevin Quinn caught a glimpse of cars that apparently were caught in the crossfire. The KTRK reporter tweeted photos of vehicles parked near the scene with bullet-riddled windshields and shattered glass.
Parking lot became triage scene
Early reports indicated the shooting took place in a strip mall parking lot near the corner of Weslayan Street and Bissonnet Street in southwest Houston.
Montalvo later said it's possible the shooting had occurred on a nearby street.
"As the victims left, the ones that could, possibly, came to this location," she told reporters at a press briefing near the strip mall.
After the shooting, CNN affiliates reported that the parking lot became a triage scene where first responders treated the wounded.
An emergency alert
from the city told people to avoid the area and warned residents to take shelter in place. Hours after the shooting, officials told residents the shelter-in-place warning had been lifted
and asked the public for help tracking down information about what happened.