DHS wouldn't say how many children are in Border Patrol custody.
After an agent noticed Felipe coughing, father and son were taken to an Alamogordo hospital, where Felipe was diagnosed with a common cold and found to have a fever of 103 degrees Fahrenheit (39.4 degrees Celsius), CBP has said. He was discharged at midday, with prescriptions for ibuprofen and the antibiotic amoxicillin.
But later that evening, the boy began vomiting and was transferred back to the hospital.
The boy, identified by Guatemalan officials as Felipe Gomez Alonzo, was the second child to die in CBP custody this month.
Guatemalan officials have been notified of the death, CBP said.
Earlier this month, the Department of Homeland Security said a 7-year-old Guatemalan girl, Jakelin Caal Maquin, had died hours after being taken into Border Patrol protection.
Lucas added that Agustin thought taking Felipe to the US would give him more "opportunity", so he took him along with some clothing, new shoes and all the money he had.
CBP typically holds children for no more than a few days. But like others in the rural farming village of Yalambojoch, he decided that traveling with a child was the only way out.
González Morales has twice requested an invitation from the USA government for an official visit but said he has not received a reply.
U.S. won't be world's 'policeman,' Trump says during Iraq visit
He is back on Air Force One and will make an another stop, which has not been announced , on his way back to Washington. The trip also comes after Trump announced that he was pulling USA forces out of neighboring Syria.
But shortly after being detained by US border agents, she developed a high fever and died of shock from sepsis on December 8.
The father of the 8-year-old Guatemalan boy who died in US government custody says his son had shown no signs of illness before falling sick Monday, the same day he died.
She said the family would ask the US government for two things: Return Felipe's body so that they can bury him in Guatemala, and let his father work in the United States so that "my brother's death won't be in vain".
It is the second time this month an immigrant child has died while being detained after crossing the US-Mexico border.
"Conducting an official visit to the country would allow me to get first-hand, direct information about the situation of migrant children, especially on those who are being held in detention", he said.
The latest fatality prompted sharp criticism from some Democrats, and US Department of Homeland Security Secretary Kirstjen Nielsen announced policy changes on Wednesday aimed at preventing future deaths of children in custody.
DHS did not immediately release more details on the trip or who Nielsen met, saying it was closed to the press.
He crossed the border along with his father and they were detained 3.29 miles from the port of entry in El Paso, Texas, on December 18.
But the Trump administration said Caal's death showed the danger of her journey and the family's decision to cross the border illegally.