"Border Patrol Officer killed at Southern Border, another badly hurt," Trump said in a tweet. "We will seek out and bring to justice those responsible. We will, and must, build the Wall!"
Trump's remarks were in response to the death of 36-year-old Rogelio Martinez, a border patrol officer who reportedly died of injuries he sustained while on duty, Xinhua news agency reported.
Martinez's partner was also injured and remained in serious condition in hospital. The two men were reportedly responding to activity near the southern border in Texas.
In a statement, Acting Secretary of Homeland Security Elaine Duke said Sunday that the agency is "fully supporting the ongoing investigation to determine the cause of this tragic event."
It is one of Trump's major campaign promises to build a wall along the US border.
Since taking office, he has repeatedly renewed his call for beefing up border security with measures, including building a wall.