Abbott, in a post on Twitter, said he will pardon Daniel Perry, 37, a U.S. Army sergeant, as soon as a request from the parole board "hits my desk."
The Republican governor noted that he can grant pardons only on the recommendation of the state's Board of Pardons and Paroles, but that he is allowed to request pardons.
The case hinged on whether the shooting was in self-defense. A jury found on Friday that Perry, who is white, shot and killed Garrett Foster, a 28-year-old white man, who was carrying an AK-47, according to the Austin American-Statesman newspaper.
Perry was driving in the city the night of the shooting and turned his Uber vehicle onto a street where a Black Lives Matter crowd was marching, according to media. Perry stopped, and several protesters including Foster approached his vehicle. Protesters told police that they feared they were being assaulted with the vehicle, according to media accounts.
Perry's defense team claimed the weapon was leveled at him and he had no choice but to fire his pistol in self-defense, the newspaper reported. Neither of Perry's attorneys was immediately available for comment by phone or email.
Perry was convicted of murder after the jury deliberated for 17 hours in the eight-day trial, according to media accounts.
"I will work as swiftly as Texas law allows regarding the pardon of Sgt. Perry," Abbott wrote on Twitter.
"Texas has one of the strongest ‘Stand your ground’ laws of self-defense that cannot be nullified by a jury or progressive district attorney," he said. "Additionally, I have already prioritized reining in rogue District Attorneys, and the Texas Legislature is working on laws to achieve that goal."
Jose Garza, the district attorney for Travis County, where the case was tried and where Austin is located, is a Democrat, and has been in office since Jan. 1, 2021.
When the verdict was read, Perry buried his head into the chest of one of his lawyers and sobbed, the Austin-American Statesman reported.
"We’re happy with the verdict. We’re very sorry for his family as well. There’s no winners in this," said Stephen Foster, the victim’s father, according to the newspaper.
Perry faces life in prison and is due to be sentenced by State District Court Judge Clifford Brown on Tuesday, according to online court records for the 147th District Court in Travis County, Texas.