President Trump has renewed his call for a wall along the US border with Mexico following the death of Rogelio Martinez, a Texas border guard, and another in an attack.
Trump confirmed on Twitter that the perpetrators will be searched for bringing them to justice, stressing "we will build the wall, it must be."
The two policemen were assaulted while they were on duty near the town of Van Horne, 193 km from the border town of El Paso.
The Border Police Special Operations Group and members of the customs and border protection forces in the region have searched for potential suspects.
Acting Secretary of Homeland Security Ellen Duck said the ministry "fully supports ongoing investigations into the cause of this tragic event."
Texas Representative Ted Cruz expressed his condolences to Martinez's family and friends, adding that what happened was proof of the threat posed by unsafe borders to US communities and those responsible for defending them.
President Donald Trump signed an executive order in January directing the Department of Homeland Security to design and build the wall on the southern border.
The construction of the border wall is the main promise made by Trump during his campaign to combat illegal immigration and prevent drug trafficking.