US Democrats have demanded an inquiry after a 16-year-old migrant died on Monday at a detention centre on the border with Mexico.
Carlos Gregorio Hernandez Vásquez is the fifth child to die after being held since December.
Democratic Texas congressman Joaquin Castro spoke of an "epidemic of death" in the border area.
President Donald Trump has vowed to clamp down on illegal immigration at the southern border.
In February, Mr Trump declared a national emergency to appropriate funds for a border wall.
There has been an increase in migrants trying to cross the frontier this year, and border agents say they are struggling to process the numbers.
What happened to Carlos?
Border agents apprehended the Guatemalan teenager for illegally crossing the border on 13 May and took him to a central processing centre in McAllen, Texas. He was travelling alone.
On 19 May, the teenager was diagnosed with flu and given medicine. He was transferred to the Welasco Border Patrol Station, reportedly in order for the illness to be contained.
On Monday, he was found unresponsive. An official cause of death has not been announced.
The day after his death the US Customs and Border Protection (CBP) announced the McAllen centre had been temporarily closed after a "large number" of those held began to show flu-like symptoms.
The centre will not take any more migrants for the moment "to avoid the spread of illness", the CBP said.
A brother of Carlos in New Jersey told broadcaster CBS News of his shock, that he would die in a country where he had come for a better life.
Under federal law, minors should normally be transferred to a Health and Human Services (HHS) shelter within 72 hours of their detention.
An HHS spokesman told the Associated Press news agency that a "minority of cases exceeding 72 hours have generally involved exceptional circumstances".
What do we know about the four other deaths?
All of the children who have died thus far have come from Guatemala.
In December, Jakelin Caal Maquin, a seven-year-old girl, died from a bacterial infection in CBP custody.
Officials say she received emergency medical attention and was revived twice before being flown to hospital in El Paso, where she died after suffering a cardiac arrest, brain swelling and liver failure.
Weeks later, on Christmas Eve, eight-year-old Felipe Gómez Alonzo died in hospital after contracting the flu.
On 30 April, Juan de León Gutiérrez, 16, also died in an El Paso hospital from a brain infection, according to Guatemalan officials.
And shortly before Carlos' death, an unnamed two-year-old died in hospital after battling a high fever and pneumonia for weeks.
What's been the reaction?
CBP acting commissioner John Sanders said the agency was "saddened by the tragic loss of this young man" and said they were "committed to the health, safety and humane treatment" of those in custody.
The Congressional Hispanic Caucus, a group of 38 Democratic members, have demanded a federal investigation into the child deaths and detention on the border.
"Nobody had died for 10 years [in detention]. And in the last six months, you've had five deaths," he told reporters.
"They're concealing the truth of these atrocities to the American people," Mr Castro told a press conference on Tuesday.
But President Trump blamed the Democratic Party for the death, saying they were making things "very, very dangerous for people" by not supporting changes to the system.
"We could have it all worked out," he told reporters.
Mr Trump unveiled immigration plans earlier this month, which favour English-speaking better-educated workers.
Democrats dismissed them as "dead-on-arrival" for failing to address the issue of "Dreamers" - people brought to the US as children who have no legal right to remain.
What's the situation at the border?
According to official statistics, more than 300,000 people were apprehended at the southern border between January and April, with numbers rising every month.
Officials say they do not have the facilities to handle the rising numbers of migrants.
Opposition lawmakers, rights groups and international charities have condemned the treatment of people at the border, pointing to cramped holding pens and shoddy accommodation.