Nielsen's comments come amid growing criticism over Attorney General Jeff Sessions' new "zero-tolerance" policy at the border to prosecute as many people as possible for illegally entering the US, even if it means tearing families apart.
She also echoed an argument made by President Donald Trump that it's in the hands of Congress to make the change.
The Associated Press reported last week that about 2,000 children have been separated from their parents at the USA and Mexican border during a six-week period in a crackdown on illegal entries according to Department of Home Security figures.
The administration wants to send a message, said Maine Senator Susan Collins, a Republican critic of the policy, "that if you cross the border with children, your children are going to be ripped away from you". His clear-eyed strategy is to use the separated children as pawns to extract concessions from Democrats on an immigration package that would include money for Trump's border wall and cuts to legal immigration, among other measures.
The outcry over children being separated from their parents at the Mexican border may have caused a rift in another family: the Trumps.
"This is not a zero tolerance policy, this is a zero humanity policy, and we can't let it go on", Democratic Sen.
Meanwhile, Texas Congressman Beto O'Rourke and former El Paso County Judge Veronica Escobar and others led a Father's Day march to Tornillo, Texas, where migrant children are being heldin a tent city detention facility.
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The push towards immigration votes in the House of Representatives is intensifying the divide among Republicans on one of the party's key issues and fuelling concerns that a voter backlash could cost the GOP control of the House in November. "And it's on all of us, not just the Trump administration, ' he said on CNN's 'State of the Union" on Sunday. USA protocol prohibits detaining children with their parents because the children are not charged with a crime and the parents are.
But in a statement from White House spokesman Raj Shah, he explained that Trump was referring to a proposal backed by Democrats that would offer a DACA fix without substantial border security funding.
"It is inconsistent with our American values to separate these children from their parents", Ms Collins said on CBS' "Face the Nation" on Sunday.
After Pope Francis tweeted "Woe to anyone who stifles [children's] joyful impulse to hope", Steve Bannon responds: "The Pope - more than anyone else - has driven the migrant crisis in Europe. the Catholic Church is one of the worst instigators of this open borders policy". And President Trump's claim that Democrats need to change the relevant law is no better.
Melania Trump's Father's Day statement emphasises the fact that laws are always applied with discretion and that the United States can be both a law-abiding country and one that "governs with heart".
White House adviser Kellyanne Conway also acknowledged the existence of the policy in an interview with NBC on Sunday, although she said "nobody" liked it. Democrats are good at only three things, High Taxes, High Crime and Obstruction. Sad!
It is the Trump administration's decision this year to prosecute all unlawful immigrants as criminals that has forced the breakup of families; the children are removed when the parents are taken into federal custody. We want you to imagine for a moment what this might be like for a child: to flee the place you have called your home because it is not safe to say and then embark on a unsafe journey to an unknown destination, only to be ripped apart from your sole sense of security with no understanding of what just happened to you or if you will ever see your family again.