Democratic representative Sylvia Garcia, whose district includes the Houston neighborhood where the shooting occurred, said acting ICE Director David Venturella told her Lorenzo Salgado Araujo "was not a target."
Salgado Araujo was a homebuilder who had lived in the US for more than 35 years, had no criminal record and was close to finishing the long process of obtaining legal status when he was killed early Tuesday morning, according to his family.
"We've got to do something. This is just one more death too many," Garcia said in an interview with MS Now. "And if we've got to bring outside, independent folks to come in and look at it, we should do that."
A spokesperson for the Department of Homeland Security did not immediately return an email seeking comment late Thursday.
DHS, which oversees ICE, previously said that federal officers were conducting a targeted operation to arrest a person in the country without legal status when they attempted to stop a vehicle driven by Salgado Araujo. The agency said Salgado Araujo rammed an ICE vehicle and that a federal officer fired a weapon in self-defence.
The federal agents weren't wearing body-worn cameras, DHS said, and few photos or videos surrounding the shooting have emerged publicly in the days since the encounter, unlike other deaths involving federal immigration officers.
DHS said the agents at the scene in Houston had not yet been issued body cameras, which it blamed on Democrats and a record government shutdown that was fuelled by President Donald Trump's immigration crackdown.
US Rep. Christian Menefee, a Democrat who also represents Houston, said if the agents didn't have the devices, it was because Trump and Republican lawmakers did not want them to be carrying them.
"Houston is done accepting excuses from an agency that has more money than it knows what to do with and still can't manage basic accountability," he said in a statement.
The Harris County District Attorney's office said it would conduct an investigation into the shooting. The office is consulting with local prosecutors in Minneapolis, where federal agents fatally shot two US citizens, to learn how they have navigated investigations into federal immigration agents, spokesperson Rafael Lemaitre said.
Three men, including Salgado Araujo's brother, were detained by ICE during the fatal traffic stop, according to Juan Proaño, CEO of the League of United Latin American Citizens, who has been communicating with their families.
In the aftermath of the fatal Minneapolis shootings of Renee Good and Alex Pretti, Democrats had refused to fund ICE and the Border Patrol without changes to those operations designed to increase accountability and transparency. Republicans in Congress eventually passed legislation funding just ICE and CBP for three years.