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A heart-breaking photo of a Salvadoran man and his toddler daughter face-down in the water after drowning in a desperate attempt to reach America has highlighted the tragedy of the US migrant crisis.

The man, named by media as Oscar Alberto Martinez, lies face down in shallow water on the bank of the Rio Grande. His two-year-old girl, Valeria, is tucked inside his shirt and his right arm is around her neck.

The bodies of father and daughter were photographed on the Mexican side of the Rio Grande, near Matamoros, across from Brownsville, Texas, on Monday.

The searing picture, taken by journalist Julia Le Duc and published in Mexican newspaper La Jornada, highlights the perils faced by mostly Central American migrants hoping to find asylum in the US. It is also reminiscent of the 2015 image of a three-year-old Syrian boy who drowned in the Mediterranean near Turkey, which focused international attention on the Syrian exodus.

The bodies of Oscar Martinez and his toddler daughter Valeria. Photo: AAP

America’s Associated Press said Mr Ramírez had decided to swim across the river after becoming frustrated because he and his family could not present themselves to US authorities and request asylum.

He left 23-month-old Valeria on the US side of the river and started back to get his wife, Tania Vanessa Avalos. But the little girl threw herself into the water and she and Mr Martinez were both swept away in the current when he tried to save her.

Le Duc told AP their story was based on Ms Avalos’s account – “amid tears” and “screams” – to police at the scene.

Mexican local government officials have confirmed the incident, but won’t discuss it publicly. Back in El Salvador, Mr Martínez’s mother, Rosa Ramirez, said she had also spoken to Ms Avalos.

“When the girl jumped in is when he tried to reach her, but when he tried to grab the girl, he went in further … and he couldn’t get out,” Ms Ramírez told AP.

“He put her in his shirt, and I imagine he told himself, ‘I’ve come this far’ and decided to go with her.”

The US-Mexico border has long been a sometimes deadly crossing. AP said 283 migrant deaths were recorded there last year; a toll for 2019 has not been released.

In recent weeks alone, two babies, a toddler and a woman were found dead on Sunday, overcome by sweltering heat; elsewhere three children and an adult from Honduras died in April after their raft capsized on the Rio Grande; and a six-year-old from India was found dead earlier this month in Arizona, where temperatures routinely soar into the high 30s.

The search for Mr Martínez and his daughter was suspended on Sunday due to darkness. Their bodies were discovered the next morning, hundreds of metres from where they had tried to cross – and just a kilometre from an international bridge.

Ms Ramirez told AP her son and his family left El Salvador on April 3. They spent about two months at a shelter in Tapachula, near Mexico’s border with Guatemala.

“I begged them not to go, but he wanted to scrape together money to build a home,” she said. “They hoped to be there a few years and save up for the house.”

Mexican President Andres Manuel Lopez Obrador said the drownings were “very regrettable”.

“We have always denounced that as there is more rejection in the United States, there are people who lose their lives in the desert or crossing” the river, he said.

There was no immediate comment from the White House.