The attorney general's office identified the two injured officers as Capt. Wes Hensley and Sgt. Mark Rychen. They're part of the fugitive apprehension unit. Sgt. Rychen was sent home from the hospital. Capt. Hensley was shot in the leg, torso and face.
Paxton said his officer who remains in the hospital is in good spirits. The officer will require additional surgery this week at Ben Taub Hospital.
Paxton asked all Texans to pray for the injured, following the violent confrontation.
Texas' Attorney General released this statement Tuesday night:
"This afternoon, Captain Wes Hensley and Sergeant Mark Rychen from the Fugitive Apprehension Unit in my office were shot and wounded while serving an arrest warrant on a suspect in Northeast Harris County. A deputy from the Harris County Sheriff's Department was also shot. These brave and courageous law enforcement officers were fulfilling their call to duty to apprehend a known criminal with a dangerous past. Thankfully, all of the injured law enforcement officers appear to be recovering well this evening. I'm asking all Texans tonight to pray for those recovering, their families, and all the men and women in law enforcement who face unpredictable dangers each day to keep Texans safe."
Harris County deputy undergoing surgery after shootout with suspect; 1 officer released and 1 still hospitalized
James Robert Smejkal III, a Harris County Sheriff's deputy, was also shot and was undergoing surgery Wednesday morning. He is a 29-year veteran with the agency. Smejkal's son told ABC13's Courtney Fischer that the bullet is still lodged in his father's forearm.
"My uncle Jim is one of the best guys I know. And just to have him put his life on the line, along with the other officers, it's just amazing. We don't give them enough credit," said Michael Netek, Smejkal's nephew.
After the shootout, Trevino was found dead Tuesday evening of an apparent self-inflicted gunshot wound inside the home on Hartwick Road after an hours-long standoff. The shots before that were captured on camera.
WATCH: Witness captures dramatic video of shootout
Witness captures dramatic video of standoff in NE Harris County
You can hear the labored breathing of an eyewitness on that video, watching and living through the heart-racing moments of the SWAT standoff.
You can see what appears to be lawmen huddled behind a black car. Seconds later, a frantic call for help goes out.
"Hey! Call EMS. We're going to need additional units."
Gunfire erupts, then yelling before the eyewitness makes a desperate dash to safety.
SEE ALSO: What we know about shootout suspect Daniel Trevino
Ambulance with injured deputy escorted to medical center
Our news crews were right there on the ground, capturing powerful images as paramedics rushed one of the injured officers to the hospital.
"One of them was shot in the foot," said Major Mike Lee, of the Harris County Sheriff's Office. "The other agent was shot numerous times, torso, leg and face."
Another deputy was injured in a motorcycle crash while on the way to assist at the scene, but has since been released from the hospital.
"We feel blessed that they're going to be okay," Lee said.