DALLAS -- An NFL player said Monday he accepts the apology offered by a Dallas police officer who stopped him with a drawn gun in a hospital parking lot while his mother-in-law was dying inside.

Houston Texans running back Ryan Moats said on ABC's "Good Morning America" that he hopes Officer Robert Powell was sincere in his apology.

Powell stopped Moats' SUV outside Baylor Regional Medical Center in suburban Plano on March 18 after the vehicle rolled through a red light. Moats' wife, Tamishia, and other relatives were also in the car.

The officer pulled out his gun and threatened Moats with jail as the player pleaded to be allowed to go inside the hospital. Moats' mother-in-law, 45-year-old Jonetta Collinsworth, died before he got there, while Powell wrote Moats a ticket and lectured him.

"I loved Jo ... my mother-in-law. We call her Jo. She was just like my mom basically," Ryan Moats said.

Powell, who first apologized in a statement Friday through his attorneys, repeatedly said in an interview with Dallas-Fort Worth television station KTVT aired Monday night that he made mistakes in the stop.

Powell said he didn't know why he didn't allow Moats to go into the hospital once he realized what was happening.

"I should have. Again, I don't know why I didn't do that and I should have. That was my mistake," Powell told KTVT.

He also said he didn't know why he spoke to Moats the way he did.

"That was my mistake. All I was trying to do was get him to calm down."

Powell, who has been placed on paid leave pending an investigation, said he didn't know what his punishment should be but he hoped he wouldn't lose his job.

Tamishia Moats said earlier Monday she'd like to hear the apology personally, but that she, too, would definitely accept it.

Later Monday morning, Ryan and Tamishia issued a statement through the Texans.

"The Moats family would like to thank the public for all their support and for expressing their condolences during this difficult time," the statement read. "We will now be focusing on our family and healing during this time of grievance."

Powell said Monday night he hoped to have the chance to meet with the couple.

According to video from a dashboard camera inside the officer's vehicle, Tamishia Moats and another woman disregarded Powell's order to get back inside their vehicle, and they rushed into the hospital.

Powell yelled at Tamishia Moats to stay in the SUV.

"Excuse me, my mom is dying," Tamishia Moats said before going into the hospital. "Do you understand?"

Tamishia Moats told Dallas-Fort Worth television station WFAA on Monday that she was reacting instinctively. She was by the side of her mother when Collinsworth died a short time later from breast cancer.

"He could have shot me. But at that time I was only thinking about my mom," she said.

Ryan Moats said the officer pointed his gun at his wife and then at him.

"My first thought was 'Man, just stop. Don't move,'" he told WFAA. "'Cause I didn't want anything worse to happen."

Powell said he didn't recall pointing his weapon. "When I found that there was no threat, I did reholster my weapon immediately."

Moats explained that he had waited until there was no traffic before continuing through the red light. When Powell asked for proof of insurance, Moats grew more agitated and told the officer to go find it.