The picture of Oscar Alberto Martinez, 25, and his 24-month-old daughter Angie Valeria put a renewed focus on the plight of refugees and migrants who are mostly from Central America.
The shocking image 2-year-old girl clinging with her dad's neck, the young girl found tucked inside her father's T-shirt.
The photograph was taken by journalist Julia Le Duc, who lives in Mexico.
For months, advocates have been warning that deaths at the border would increase as migrants are forced to cross in more risky areas by U.S. policies that make it harder for those seeking asylum to turn themselves in at ports of entry. Martinez' wife, Tania told Mexican authorities she watched her husband and child disappear in the strong current.
Mr Martinez caught hold of Valeria, but both were swept away by the current. The account was based on remarks by a tearful Avalos to police at the scene.
"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", Martinez" mother, Rosa Ramírez told the AP reporter in a phone interview. "He put her in his shirt and I imagine he told himself, "I've come this far" and chose to go with her".
The area has had problems with gang violence but these days it "is calm", she said, adding that he never had any problems with gangs - they left for economic reasons.
The farther reportedly hoped to find a job to support his family and buy a house, his mum said.
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El Salvador's Foreign Ministry said it was working to assist the family including Ms Avalos, who was at a border migrant shelter following the drownings.
President Nayib Bukele of El Salvador expressed sorrow for the deaths and began procedures for repatriating the bodies. Martinez first crossed the river with Angie and left her on the US side near Brownsville, TX.
She called on those who plan to migrate to the United States illegally to refrain from doing so.
A photo of a drowned father and his two-year-old daughter at the US-Mexican border surfaced on Wednesday.
"As his administration refuses to follow our laws - preventing refugees from presenting themselves for asylum at our ports of entry - they cause families to cross between ports, ensuring greater suffering & death". The family obtained a humanitarian visa from the Mexican government and was waiting in a migrant camp before desperation kicked in and they attempted to cross the river on their own. This follows outrage over US officials returning more than 100 migrant children to a facility where they reportedly lived in inhumane conditions. "People are coming up, they're running through the Rio Grande", he said, referring to the river known as the Rio Bravo in Mexico that forms a large part of the border between the two countries.
The family had been waiting in a migrant camp in Matamoros for an appointment to receive political asylum from the United States, the newspaper said, citing Martinez's wife.