The Pope has said he is "profoundly saddened" by the haunting image of a migrant father and his baby daughter who drowned in the Rio Grande while attempting to cross from Mexico to the US on Sunday.

The image, captured on Monday, shows Oscar Alberto Martínez, 25, and his 23-month-old daughter, Angie Valeria, lying face down in the reeds.  The picture shows the pair wrapped in his T-shirt and with Angie's arm still draped over his shoulder.

His wife, Tania, watched helplessly from the other shore as the pair were swept away by a strong current. The bodies came ashore on the Mexican side of the border, opposite Brownsville, Texas, and are to be repatriated to El Salvador, where the young family came from.

They had been trying to swim across the river to reach the US when the tragedy happened.  It is reported that they had wanted to apply for asylum but decided to take their chances crossing the Rio Grande because of the lengthy application process.

Julia Le Duc, the photographer who captured the image of the pair, told CNN that the father and daughter had actually made it safely to the other side of the river, but when Martínez went to go back and get his wife, Tania Vanessa Avalos, his young daughter followed him into the water.  

"With immense sadness, the Holy Father has seen the images of the father and his baby daughter who drowned in the Rio Grande River while trying to cross the border between Mexico and the United States," said Alessandro Gisotti, the ad interim Director of the Holy See Press Office. 

"The Pope is profoundly saddened by their death, and is praying for them and for all migrants who have lost their lives while seeking to flee war and misery."

Martínez's grieving mother, Rosa Ramirez, said she had tried to talk her son out of going to the US but it was his dream to go there and "build a good future for his family". 

In the wake of his death, she said she feels a hole that "nobody can fill, but God gives me strength".