Martinez and Valeria were swept away by the border river between Matamoros, Mexico, and Brownsville, Texas, on Sunday, and their bodies were found the next morning.

The photograph of them face down along the bank with the girl tucked inside his shirt and her arm draped over his neck underscored the perils that migrants and asylum seekers face in trying to reach the United States.

The acting secretary of Homeland Security said he expecteded 25 per cent fewer migrants to cross the border this month, as officials in Yuma, Arizona unveiled the newest temporary facility meant to detain children and families.

That number of illegal crossings would still be too high, but it was a start, Kevin McAleenan said, crediting Mexico with a concentrated effort to stop Central Americans before they arrived even to Mexico - a push prompted by threats of tariffs from President Donald Trump.

The president has seen numbers of migrants crossing the US-Mexico border skyrocket under his term despite his hardline policies and tough talk.

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More than 100,000 people, mostly families from Central America, have crossed the border each month over the past few months.

Trump sees the monthly border numbers as a benchmark for success, and in the past when he felt numbers were too high, he threatened to shut down the border.

McAleenan dismissed the idea that a projected decrease in June was due in part to hot summer months, traditionally a time fewer people cross.

"These initiatives are making an impact," he said.

Meanwhile, facilities that house detained migrants are vastly overcrowded and advocates and attorneys have decried conditions inside. Border facilities are meant as temporary holding stations, built to hold a maximum of about 4000, but have routinely held as many as 15,000.

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Teens and children, detained days or weeks by US border authorities, described frigid cells where flu-stricken children in dirty clothes ran fevers, vomited and cried with no idea when they would get out, according to court documents in a case that governs how children are cared for in government custody.

Congress sent Trump a $4.6 billion ($6.5 million) package on Thursday that bolsters care for the tens of thousands of migrants taken into custody. McAleenan praised the move, but also cautioned there was much more work to do.

The deaths of Oscar Alberto Martinez Ramirez and daughter Valeria, meanwhile, have moved people in Matamoros who've faced similar decisions.

Viviana Martinez, a pregnant woman who left Cuba with her husband and toddler son, said they had seen the picture online and it had "broken the hearts" of the migrant community there.

She confessed that a few days earlier, she stood on the grassy riverbank trying to map out how she might make it.

"I'll be honest. A few days before this terrible accident I was thinking (about it) out of desperation. ... I was even looking at how to cross, but thank God I stopped myself because I didn't want to risk the life of my child," Martinez said.

AP