not taken away from her mother at the US border, says her father.
A photograph of the Honduran toddler sobbing in a pink jacket was taken at the scene of a border detention.
Time magazine has used the image for its latest cover, depicting President Donald Trump looming over the girl with the caption: "Welcome to America".
But she is not one of the thousands of child migrants taken from parents.
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The image was taken by a photographer for the news agency Getty Images, John Moore, on 12 June at McAllen, Texas.
The Pulitzer prize-winner told the BBC that the mother had been breastfeeding her child after crossing the Rio Grande in a raft in the moments before they were detained.
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Image caption
Denis Valera (L), Sandra Sanchez (R) and Yanela Denise (M). Mr Valera says the couple have three other children who are back in Honduras
Mr Moore said they were taken away together by border patrol.
The photo stoked outrage over the Trump administration's child migrant separations policy, rolled out in April, of removing young undocumented people from their mothers and fathers as they are detained for crossing the US-Mexico border.
The photo helped secure $17m (£13m) in donations from hundreds of thousands of people on a Facebook fundraiser for the Refugee and Immigrant Center for Education and Legal Services, a Texas-based non-profit organisation.
Media captionA Guatemalan asylum seeker is reunited with her son at a Baltimore airport
"My daughter has become a symbol of the separation of children at the US border," Denis Valera told Reuters news agency.
"She may have even touched President Trump's heart."
"Seeing what was happening to her in that moment breaks anyone's heart," he added.
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Image caption
Sandra Sanchez (L) with her daughter Yanela Denise at the border
Mr Valera said his daughter and her mother, Sandra Sanchez, have been detained together in the border town of McAllen as Ms Sanchez seeks asylum.
Honduran Deputy Foreign Minister Nelly Jerez verified Mr Valera's version of events to Reuters.
The Border Patrol agent who stopped Ms Sanchez and her daughter, Carlos Ruiz, said the mother was asked to set the child down so she could be searched.
"The kid immediately started crying as she set her down. I personally went up to the mother and asked her, 'Are you doing OK? Is the kid OK?'
"And she said, 'Yes. She's tired and thirsty. It's 11 o'clock at night.'"
The little girl is two-year-old Yanela Denise, according to the Daily Mail newspaper.
Mr Valera said Ms Sanchez and their daughter had left the Honduran city of Puerto Cortes without telling him or the couple's three other children.
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He said he believed she went to the US to search of better economic opportunities.
Mr Valera told Reuters: "If they are deported, that is OK as long as they do not leave the child without her mother. I am waiting to see what happens with them."
He told the Daily Mail he understands Ms Sanchez paid $6,000 (£4,500) to a smuggler to get her across the border.
According to the newspaper, the couple's three other children are aged 14, 11 and six.
Mr Valera said: "The kids see what's happening. They're a little worried but I don't try to bring it up that much. They know their mother and sister are safe now."