In a statement expressing condolences for the San Antonio officer's family, Abbott mentioned the Police Protection Act. It's a bill he hopes is passed into law in the next legislative session, which begins in January.
Tom Moore with the Harris County Fraternal Order of Police said he believes that measure is a good idea.
VIDEO: San Antonio police officer killed while writing ticket
"Law enforcement officers are humans, too. We have families and concerns. We also have the same rights as everybody else and people are trying to take those rights away just because we have the obligation to serve and protect them," Moore said.
Ray Hunt with the Houston Police Officers Union said his organization called for the department to allow officers to patrol with partners upon request after the attack on Dallas officers this summer. Hunt said those requests have been accommodated by the department so far.
Governor Abbott's full statement:
"Cecilia and I extend our deepest condolences to the victim's family and harshly condemn this horrific act of violence. We ask that all Texans join us in praying for the officer's loved ones as they deal with the aftermath of this unimaginable tragedy. Attacks against law enforcement officers will not be tolerated in Texas and must be met with swift justice, which is why I look forward to signing my Police Protection Act into law - making targeted attacks against law enforcement a hate crime."