New medical checks have been carried out on nearly every child in Border Patrol custody, US immigration authorities have said.
These checks follow the death of a second youngster in the agency's care in the space of less than three weeks.
An eight-year-old boy, identified by Guatemalan authorities as Felipe Gomez Alonzo, died on Christmas Eve just before midnight.
He had been in the custody of US Customs and Border Protection (CBP) with his father, Agustin Gomez, since December 18.
CBP said in a statement that an agent first noticed the boy had a cough and "glossy eyes" at about 9am on Monday.
He was taken to hospital twice that day before he died, the agency said.
The cause of death was under investigation.
Officials at the Department of Homeland Security (DHS) told reporters on Wednesday that almost all checks ordered in reaction to the boy's death had been completed.
Some children detained in more remote areas were re-screened by emergency medical technicians or Border Patrol agents, officials said.
In other places, some children were taken to medical facilities.
DHS would not say how many children were in Border Patrol custody and authorities have not disclosed the results of the examinations.
The agency also would not say why Felipe and his father were detained for almost a week, an unusually long time, or why they were placed back in detention, at a Border Patrol road checkpoint, after being released from the hospital.
Another Guatemalan child in US custody, seven-year-old Jakelin Caal, died on December 8 and was returned to her village for burial.
Her death, which brought down heavy criticism on US immigration authorities, is also under investigation.
Immigration advocates and human rights groups sharply criticised CBP in the wake of Felipe's death.
Margaret Huang, executive director of Amnesty International USA, said the Trump administration's "policies of cruelty toward migrants and asylum seekers at the border must cease immediately before any more children are harmed".
CBP said in a statement on Tuesday that it needed the help of other government agencies to provide health care.
The agency "is considering options for surge medical assistance" from the Coast Guard and may request help from the US Department of Health and Human Services (HHS), the Department of Defence and the Federal Emergency Management Agency.
With border crossings surging, CBP processes thousands of children, both alone and with their parents, every month.
According to CBP statistics, border agents detained 5,283 children unaccompanied by a parent in November alone.
Agents last month also apprehended 25,172 "family units", or parents and children together.
CBP typically holds children for no more than a few days.
Youngsters who arrive unaccompanied are turned over to longer-term facilities operated by the HHS.
The Associated Press reported this month that 14,300 children were being detained by HHS, most in facilities with more than 100 children.
CBP issued a timeline of what it said happened before Felipe's death.
Felipe was taken with his father to a hospital in Alamogordo, New Mexico, where he was diagnosed with a common cold, according to the timeline.
The boy was released just before 3pm, about 90 minutes after he had been found to have a fever of 39.4C (103F), CBP said.
He was prescribed the antibiotic amoxicillin and the pain reliever and fever-reducer ibuprofen, and was taken with his father to a holding facility at a highway checkpoint.
Around 7pm, agents helped clean up the boy's vomit. CBP said the father "declined further medical assistance" then.
The agency said its officers repeatedly conducted welfare checks on Felipe and his father, and that agents decided to take the boy back to the hospital at about 10pm because he "appeared lethargic and nauseous again".
CBP typically detains adult immigrants for no more than a few days when they cross the border before either releasing them or turning them over to US Immigration and Customs Enforcement for longer-term detention.
Agency guidelines say immigrants generally should not be detained for more than 72 hours in CBP holding facilities, which are usually smaller and have fewer services than Immigration and Customs Enforcement detention centres.