"We're in the minority right now, so when we are in the majority Speaker-Designate Nancy Pelosi has been clear that there must be an independent investigation and that Congress would investigate this," Lujan said on Tuesday.
Congress must assess what could have been done to prevent Caal's death and to guard against such tragic incidents in the future, he said.
US lawmakers were assured by CBP officials that no more migrant children have died in their custody, the congressman said.
Last Friday, CBP’s Office of Professional Responsibility and the Department of Homeland Security's Inspector General launched investigation into Caal's death. However, Democratic lawmakers are calling for an independent investigation.
READ MORE: Trump Defends Migrant Family Separation After Child's Death While in US Custody
Jakelin Caal Maquin became ill after being apprehended on December 6 for illegal entry into the United States. She was flown from Lordsburg to the nearest trauma center in the Texas city of El Paso, but doctors were unable to save her. Caal had brain swelling and liver failure, according to CBP.
Lawyers representing the Caal family said in a statement on Saturday that she was in good condition when she crossed the US border and was arrested by Border Patrol agents.
On Friday, the White House rejected responsibility for Caal's death and said it was a senseless and needless death that was 100 percent preventable.