Bannon also offered a forceful defense of the administration's "zero tolerance" policy of filing criminal charges against illegal immigrants apprehended near the border - even if it means separating them from children they are traveling with.
But she added that "all laws" needed to be followed and called upon "both sides of the aisle" to "come together to achieve successful immigration reform".
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 USA, even if it means tearing families apart.
Trump has said in recent days that Democrats should agree to his panoply of immigration measures, including full financing for a border wall and revamping the system of legal entry to the country, in effect making clear that any legislation addressing family separation must also include his priorities.
First lady Melania Trump "hates" to see families separated at the border and hopes "both sides of the aisle" can reform the nation's immigration laws, according to a statement Sunday about the controversy over separation of immigrant parents and children at the U.S. -Mexico border.
A Guatemalan woman and her infant daughter seeking asylum sit at a Catholic Charities relief center on Sunday, June 17, 2018 in McAllen, Texas.
She called on Congress to simultaneously address Trump's border wall and the fate of the young immigrants left in limbo after the president rescinded the Deferred Action for Childhood Arrivals (DACA) program.
"I hate the children being taken away", Trump told reporters Friday.
"Tearing children away from parents who have made a unsafe journey to provide a safe and sufficient life for them is unnecessarily cruel and detrimental to the well-being of parents and children", Bishop Kenneth Carter, president of the Council of Bishops of the United Methodist Church, said in a statement.
Pelosi will join members of the Congressional Hispanic Caucus in a Monday visit to the Southern California border, where she plans to talk to parents who have been separated from their children.
Mexico upset World Cup holders Germany
Joachim Low has admitted that his Germany side weren't at the races after they slipped to a disappointing 1-0 defeat to Mexico on Sunday .
"There is nothing more human than doing everything you can for your child when they face in some cases certain death, rape, torture to take them in your arms and bring them to safety", he said. And Kirstjen Nielsen, the Secretary of Homeland Security, took to Twitter in an attempt to clarify the policy.
Mr Trump plans to meet with House Republicans on Tuesday to discuss pending immigration legislation amid an election-season debate over an issue that helped vault the NY real estate mogul into the Oval Office in 2016.
Trump has placed blame for the policy on Democrats as recently as Friday, when he had an impromptu press conference outside the White House. It was focused on freeing and otherwise helping children who come to the border without a parent or guardian.
Representative Adam Schiff said the practice was "deeply unethical" and that Republicans' refusal to criticise Mr Trump represented a "sad degeneration" of the party, which he said had become "the party of lies". Jerry Nadler, live-tweeted their drama as they were stuck in the lobby of the Immigration and Customs Enforcement detention facility in Elizabeth, N.J., trying to get in to speak with detainees.
On Saturday, Trump was more direct: "Democrats can fix their forced family breakup at the Border by working with Republicans on new legislation, for a change!"
This awfulness is happening because of Attorney General Jeff Sessions' "zero tolerance" immigration policy.
In response to the rally, Denham released a statement to The Washington Post expressing optimism that the Republican House bill would end the practice.
The disclosure marks the first time the Trump administration has specified how many immigrant children have been affected by the policy.
"If the Democrats are serious, and if a lot of Republicans are serious, they'll come together", she said.