Trump has been stoking fears about a caravan of migrants in Central America who are trying to make their way to the US border.
"Trump should be more humanitarian", she said. "Go back to your Country and if you want, apply for citizenship like millions of others are doing!" tweeted the President.
The DHS request could require deploying between 800 and 1,000 active-duty troops, two United States officials said, speaking on condition of anonymity.
The migrants, who number in the thousands and include many women and children, are fleeing poverty and violence in Honduras and Guatemala, and are trekking through Mexico in hopes of reaching the US border.
In April, frustrated by lack of progress on the wall, Trump ordered the National Guard to help secure the border.
"It's hard, and we know this country is unsafe too, but back in Honduras it's even more risky, they kill for nothing", said Josena Anibal Mejia, 27, as he walked with his daughter.
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Asked if the troops would be armed, Nielsen said Mattis would decide the rules of engagement, but added: "We do not have any intention right now to shoot at people".
On Monday, Trump said in a tweet that he'd alerted the military that the situation was a "National Emergy" - but the Pentagon said then that they'd received no new orders to provide troops for border security. Most are Hondurans, seeking to escape poverty and violence, and include families with children.
Mr Mattis is responding to a request from President Donald Trump, who said he is "bringing out the military" to address what he called a national emergency. But the longer-term implications could be more profound, potentially shutting down altogether an avenue - permitted under both USA and global law - that many people fleeing violence and persecution use to take refuge here.
"If someone migrates to the United States, it's to work, and working is not a crime", he said. "They will not be allowed to stay". Those troops are under the control of state governors and are limited to support roles such as providing surveillance.
One piece of the action under consideration would use an authority similar to that invoked by the travel ban, which would block entry to unauthorized immigrants who are not yet in the US, said the three sources. "The president should not be using the military to further a partisan agenda".
"Except that I rarely use a cellphone, & when I do it's government authorized".