Attorneys for Elias Montoya announced Sunday that they are reviewing the allegations against the veteran officer and that Montoya intends to file an appeal for wrongful termination.
"Every day police officers put themselves in danger to protect the public. One of the most dangerous situations is a traffic stop on a rural road with limited radio access. It is difficult to second guess the actions of Officer Montoya without completely reviewing all of the evidence," attorney Antonia Roybal-Mack said in a statement.
Under department policy, Montoya has 30 days to appeal his firing to the Public Safety Advisory Commission, which is made up of civilians appointed by the governor.
Montoya's attorneys also said their client is thankful for the support he has received from the community.
On Sunday, several dozen people braved freezing temperatures to march through the northern New Mexico community with handmade cardboard signs.
"We support him because of who he is and what he is to this community," Taos resident Ray Martinez told KRQE.
State Police Chief Pete Kassetas fired Montoya on Friday, following an internal investigation and a disciplinary hearing.
Video from a police cruiser's dashboard camera taken during the Oct. 28 traffic stop has drawn national attention. It showed Montoya shooting at the minivan as a Memphis, Tenn., woman drove away from a traffic stop after an officer knocked out her van's window with a baton.
Montoya wrote in a police report that he aimed "at the left rear tire in an attempt to immobilize the vehicle."
The motorist, 39-year-old Oriana Farrell, had been stopped by another State Police officer for speeding. She fled twice after that officer tried to give her a ticket and then arrest her.
Farrell and her son were arrested in front of a hotel after a chase in which the van traveled at speeds of nearly 100 mph. Farrell was released on bond and faces charges of child abuse, fleeing and misdemeanor possession of drug paraphernalia for a pair of marijuana pipes that authorities say were in the van.
According to a police report, Montoya later bought the entire family food from McDonald's during the booking process.
Martinez and other supporters said Montoya, who had worked for the department for 12 years, should get his job back and that Farrell should take most of the blame for endangering her children and others as she sped through the town.
"You don't go 110 miles an hour through a school zone, putting everybody else's life in jeopardy," Martinez said.
Others in Taos have complained that police used excessive force during the stop and they are pushing for state police to change their practices. Members of the group Citizens for Social Justice plan to meet with Kassetas this week to discuss the incident.