"They wouldn't be trying", the president said. They were found on Monday near an global bridge. The mother, Tania Vanessa Avalos, who attempted to cross the river too and survived, recounted the tragic story to authorities and media outlets.
Migrant rights activists say such limits on people's access to asylum can put them in harm's way, while driving migration underground and squeezing it into new routes. Frustration with the inability to process his family's case appears to be what motivated the father to attempt the unsafe crossing.
Luckily she managed to swim back to the Mexican side of the river but was forced to watch on as her husband and daughter began to sink and were swept away.
Martinez and his daughter were met by twin disasters: fast-moving waters and an asylum system unprepared for the crush of Central Americans fleeing crime and poverty.
Frustrated because his family was unable to have an opportunity to present themselves to USA authorities and request asylum, he swam across the river with his child.
"I begged them not to go, but he wanted to scrape together money to build a home", Rosa Ramirez told AP. "You can tell he was trying to protect her".
"I hate it", Trump said when he was asked about the photo on Wednesday.
The distressing visual has come as a crude reminder of desperate measures immigrants take to enter the US.
"What we are reiterating is that we are supporting the family in any way we can and warning our fellow compatriots that the journey here is unsafe and they shouldn't put themselves at risk", Pichinte said. The pair had travelled from El Salvador and were seeking asylum in the United States.
"I'm feeling so many different things now", Ramirez said.
But he cautioned that while authorities could legally stop migrants who seek to cross, he added that it was "not a legal issue". "God help us." Bukele said his government would cover "all repatriation expenses and will help the family financially".
The number of Central Americans arriving at the US border - in caravans, alone or guided by traffickers - has jumped this year, prompting Trump to demand even tougher action from Mexico to stem the tide. Many instead choose to cross the border illegally. While it appears calm, the Rio Grande is a fast-moving river and through it flow unsafe currents.
Shortly after the image was released, the acting head of US Customs and Border Protection announced he was resigning.
On Twitter on Wednesday, Matamoros Bishop Eugenio Andrés Lira Rugarcía said that the diocese, which covers the territory where the drowning occurred, is "very sorry for the death of the migrants who have lost their lives looking for a better future".
Since the MPP program was launched in January, more than 15,000 asylum seekers have been sent back to Tijuana and two other Mexican cities, Mexicali and Ciudad Juarez.
Six children have died since September after being detained by border agents and some have blamed the policies of President Donald Trump.
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