By Ashley Killough and Clare Foran, CNN

(CNN) -- After the President of the United States spent the day openly encouraging a group of critical congresswomen of color to leave the country, the four Democratic lawmakers made clear Monday they're here to stay.

"I want to tell children across this country is that no matter what the President says, this country belongs to you," said Rep. Alexandria Ocasio-Cortez of New York at a news conference on Capitol Hill on Monday. "And it belongs to everyone and today that notion, that very notion was challenged."

Ocasio-Cortez was joined by Reps. Ayanna Pressley of Massachusetts, Ilhan Omar of Minnesota and Rashida Tlaib of Michigan, a group shorthandedly referred to on Capitol Hill as the "squad," a quartet of lawmakers who throughout their first months in Congress have found themselves at odds with leaders in their own party as well as sharply criticizing the President.

Most recently the four lawmakers have sharply rebuked the administration for the conditions at migrant detention facilities as part of the overall humanitarian crisis at the US southern border, part of a point Pressley made clear that should not be lost in the coverage of Trump's tweets.

"I encourage the American people and all of us in this room and beyond, to not take the bait," Pressley said at the opening of the news conference. "This is a disruptive distraction from the issues of care, concern and consequence to the American people."

The four lawmakers' response Monday was a serious condemnation of a President who through a series of racist tweets and remarks made false allegations about the Democratic women and said that if they were going to criticize his policies, then they can remove themselves from the country. The squad's unified reply Monday night was one of defiance.

"Our squad is big," Pressley said. "Our squad includes any person committed to building a more equitable and just world, and that is the work that we want to get back to and given the size of this squad and this great nation, we cannot, we will not be silenced."

Omar condemned the President's Twitter attack against the freshmen congresswomen as "a blatantly racist attack on four duly elected members of the United States of House of Representatives, all of whom are women of color."

Omar went on to say, "This is the agenda of white nationalists, whether it is happening in chat rooms or it's happening on national TV, and now it's reached the White House garden."

On Sunday, the President used racist language to attack progressive Democratic congresswomen, falsely implying they weren't natural-born American citizens; Omar was the only member of the four not born in the United States. On Monday, Trump stood by his racist attacks on the quartet of Democratic congresswomen, insisting they leave the United States if they continue complaining about his policies.

Omar, who along with Tlaib, made history in January as becoming the first two Muslim women in Congress, said Trump's comments evoke a familiar sentiment made to people of color.

"You might have noticed how when he said go back to where you came from there was an uproar through all of our communities, because every single person who is brown or black, at some point in their life in this country, heard that," Omar said.

Tlaib told CNN's Wolf Blitzer following the news conference that Trump is overseeing a "failed presidency." When asked by Blitzer about how Trump's supporters applauded his remarks at the White House on Monday, she replied, "No, there's more of us than them."

"There's more love," she said on "The Situation Room." "There's more love for unity, for respect for each other. There's a love that this is a nation of immigrants."

Several members of the squad visited border detention facilities in recent weeks and Ocasio-Cortez gave an impassioned testimony Friday before a House hearing when recalling her recent trip. On Monday, Ocasio-Cortez sharply rebuked Trump's handling of the crisis at the southern border.

"Weak minds and leaders challenge loyalty to our country in order to avoid challenging and debating the policy," she said.

"He can't look a child in the face and he can't look at all Americans and justify why this country is throwing them in cages," she added. "So instead he tells us that I should go back to the great borough of the Bronx and make it better. And that's what I'm here to do."

This story has been updated with additional developments Monday.