She did not say how many survivors remained in hospital, but the number could be around 11 based on initial figures that officials gave, including possibly four children.
The Department of Homeland Security announced it had opened a criminal investigation, as Biden took aim at human smuggling gangs.
“The tragic loss of life in San Antonio, Texas that took place yesterday is horrifying and heartbreaking,” he said in a statement.
“This incident underscores the need to go after the multi-billion dollar criminal smuggling industry preying on migrants and leading to far too many innocent deaths,” he said.
Federal law enforcement agents on Tuesday arrested two men at the address linked to the tractor-trailer’s registration, court documents showed.
Juan Francisco D’Luna-Bilbao and Juan Claudio D’Luna-Mendez, both Mexican nationals whose US tourist visas had expired, were illegally in possession of multiple firearms, the documents alleged.
A third person, suspected of being the driver of the tractor-trailer, was arrested nearby while “very high on meth,” reported the local daily San Antonio Express-News, citing a law enforcement officer.
According to Mexican President Andres Manuel Lopez Obrador, of the dead whose identities are known, 22 were from Mexico, seven from Guatemala and two from Honduras.
“It’s a tremendous misfortune,” he told reporters.
It was the deadliest single incident involving migrants along the southern border in memory, and drew more attention to the risks that hundreds of thousands of people face seeking to enter the United States from Mexico without permission.
On Monday, the high temperature in San Antonio was 103 degrees Fahrenheit (39.4 degrees Celsius), and the temperature in the unvented trailer would have been much higher.
By Tuesday afternoon, authorities had removed the trailer from where it had been abandoned with its human cargo, on a narrow road sandwiched between train tracks and auto junkyards.
Replacing it were makeshift crosses adorned with artificial flowers.
“I feel that if these people walk hundreds of miles to get over here, it wouldn’t hurt us to walk maybe one mile to put the crosses and candles,” said Angelita Olvera, who lives nearby.
“Hopefully, whoever had them in the trailer will pay the consequences,” she said.
San Antonio Police Chief William McManus said authorities were first alerted to the trailer by an emergency call at about 5:50 pm local time (2250 GMT) on Monday.
“A worker who works in one of the buildings up here behind me heard a cry for help,” he told reporters.
The worker “came out to investigate, found a trailer with the doors partially open, opened them up to take a look, and found a number of deceased individuals inside,” McManus said.
The tragedy came five years after 10 migrants were found dead in a trailer with broken air conditioning and clogged ventilation holes near San Antonio.
In recent weeks Border Patrol officers have discovered other attempts to bring undocumented travelers into the country in large trucks.
On June 14, 80 people from Mexico, Guatemala, Honduras and El Salvador were discovered inside a tractor-trailer when it was inspected by agents at a highway checkpoint north of Laredo, a border hub in south Texas.
Three weeks earlier, agents intercepted a trailer with 48 people inside near Sierra Blanca in western Texas.
Jesus Thompson, 60, lives just across the train track from where the people in the trailer were found.
“People from Mexico and Guatemala come here to seek the American dream,” he said.
“I would tell the people who are there and who are fleeing to think about it before coming here, because there is a tremendous risk, and especially now that the weather is very hot.”
The case immediately became a focus of politics when Republicans attacked Democratic President Biden for allegedly being soft on immigration.
“These deaths are on Biden. They are a result of his deadly open border policies,” said Texas Governor Greg Abbott.
Under Biden, more than 200,000 people attempting to enter the country illegally have been interdicted at the border each month and sent back.
But there is no good estimate of the thousands more that succeed in staying inside the country.
Biden said he had already launched an anti-smuggling campaign that focused on the networks and arrested 2,400 people in recent months.
“Exploiting vulnerable individuals for profit is shameful, as is political grandstanding around tragedy,” he said.
The migration issue will be a key agenda item when Biden hosts his Mexican counterpart Lopez Obrador for talks on July 12.