An 8-year-old boy from Guatemala died Tuesday while in U.S. custody, immigration officials announced, becoming the second child to die in such circumstances this month.

In a statement, Customs and Border Protection said the boy -- identified by the Guatemalan consul in Phoenix as Felipe Gomez Alonzo -- died shortly after midnight at the Gerald Champion Regional Medical Center in Alamogordo, N.M. The cause of death is unknown; he had received treatment at the hospital starting on Christmas Eve.

Immigration officials say an agent first “noticed that the child showed signs of potential illness” Monday and brought the boy and his father to the medical center, where the boy was diagnosed with a “common cold.”

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Prior to leaving the hospital, though, staff found a fever. They discharged the boy in the mid-afternoon with prescriptions for amoxicillin and Ibuprofen.

But later in the evening, the child “exhibited nausea and vomiting and was transferred back” to the facility for evaluation and treatment, CBP said, before dying around midnight.

Officials say the death is under investigation.

“DHS has continued to see a dramatic increase in unaccompanied children and family units arriving at our borders illegally or without authorization,” CBP added in a statement. “Consistent with existing law, these individuals are held at federal facilities pending their removal or release into the interior of the United States with a notice to appear at a court hearing.”

The death came during an ongoing dispute over border security and with a partial government shutdown underway over President Donald Trump's request for border wall funding. The White House referred questions about the latest case to the U.S. Department of Homeland Security, CBP's parent agency. CBP officers and the Border Patrol remain on the job despite the shutdown.

CBP promised "an independent and thorough review of the circumstances."

Alamogordo is about 90 miles from the U.S.-Mexico border at El Paso, Texas. Ruben Garcia, director of El Paso's Annunciation House, said Tuesday that he had no reason to believe his shelter had served the family but was waiting for further details about what happened.

According to Guatemala's foreign ministry, the father and son entered the U.S. at El Paso, Texas, on Dec. 18, then were taken to the Border Patrol's Alamogordo station Sunday. Oscar Padilla, the Guatemalan consul in Phoenix, said he was told by the boy's father in a telephone interview that the two had been traveling from their home in Nenton, a village about 280 miles from Guatemala City. They were planning to go to Johnson City, Tenn.

Padilla identified rhe father as 47-year-old Agustin Gomez, and said he remains in U.S. Border Patrol custody.

CBP typically detains immigrants for no more than a few days when they cross the border before either releasing them or turning them over to U.S. Immigration and Customs Enforcement for longer-term detention. Agency guidelines say immigrants generally shouldn't be detained for more than 72 hours in CBP holding facilities, which are usually smaller and have fewer services than ICE's detention centers.

Parents and children together are almost always released quickly due to limited space in ICE's family detention facilities.

The Guatemalan foreign ministry called for an investigation "in accordance with due process." A CBP spokesman on Tuesday did not respond to questions about the ministry's statement but previously said that the boy had been "previously apprehended" by its agents.

The body of a 7-year-old girl who died while in U.S. Border Patrol custody earlier this month – also from Guatemala -- was flown to her home country Sunday ahead of burial in her home village Tuesday.

In that case, Jakelin Caal and her father, Nery Caal, were traveling with a group of 163 migrants who arrived at the New Mexico border. After they were taken into custody Dec. 6, the father told a U.S. agent that the girl was sick and vomiting.

The father then signed a paper stating that Jakelin was in good health, but it was not clear how much he understood what it said. The form was in English, and agents read it to him in Spanish.

A bus carrying the two left the Antelope Wells port of entry for the Lordsburg station, roughly 90 minutes away. By then, according to a Customs and Border Protection statement, Jakelin's temperature had reached 105.7 degrees. Emergency medical technicians had to revive her.

She was then flown to a hospital in El Paso, where she died the next day.

Caal's death led to criticism of immigration officials by U.S. lawmakers, with five senior Democrats calling for a thorough review of their conduct. CBP announced new notification procedures in response to Jakelin's death, which was not revealed until Dec.14.

Large numbers of Guatemalan families have been arriving in recent weeks in New Mexico, often in remote and dangerous parts of the desert.

Xochitl Torres Small, a Democrat who will represent the district starting in January, called for a thorough and transparent investigation into the children's deaths and more medical resources along the border.

"This is inexcusable," she said in a statement Tuesday. "Instead of immediately acting to keep children and all of us safe along our border, this administration forced a government shutdown over a wall."

A spokeswoman for U.S. Rep. Steve Pearce, a Republican whose district along the U.S.-Mexico border includes Alamogordo, could not be reached Tuesday.

Felipe Gonzalez, the United Nations special rapporteur on the human rights of migrants, said Monday that the U.S. government's detention of children due to their immigration status violated international law.

Fox News' Amy Lieu, Sam Chamberlain and the Associated Press contributed to this report.