“Moving forward, all children will receive a more thorough hands-on assessment at the earliest possible time post-apprehension — whether or not the accompanying adult has asked for one,” Ms. Nielsen said in a statement.

Most of the circumstances surrounding the boy’s death remain unknown. It is not clear whether his health deteriorated because of neglect by personnel in the facilities, the perilous journey, or a combination of these factors.

“This crisis is exacerbated by the increase in persons who are entering our custody suffering from severe respiratory illnesses or exhibit some other illness upon apprehension,” Ms. Nielsen said. “Given the remote locations of their illegal crossing and the lack of resources, it is even more difficult for our personnel to be first responders.”

The secretary placed the blame on an immigration system that she said rewarded parents for sending their children to cross the border alone and brought few consequences for parents who bring their children with them into the country. “Our system has been pushed to a breaking point by those who seek open borders,” she said. “Smugglers, traffickers, and their own parents put these minors at risk by embarking on the dangerous and arduous journey north.”

She said that until the two deaths, of the 8-year-old Guatemalan boy late on Dec. 24 and a 7-year-old Guatemalan girl earlier this month, it had been more than a decade since a child had died in custody at the border.