(CNN) More than 80 House Democrats are sponsoring a nonbinding resolution condemning white supremacist rhetoric and violence that specifically targets immigrants.

While the resolution does not mention President Donald Trump, its supporters brought up Trump's rhetoric in a news conference on Tuesday. They repeatedly referenced his characterization of the border situation as an "invasion," as well as his use of the word "animals," which he had used to describe MS-13 gang members at a 2018 event and some took as a comment about undocumented immigrants overall.

Pressed on whether Trump should bear most of the blame for the rise of white supremacy in the United States, Rep. Tom Malinowski of New Jersey -- a freshman Democrat who introduced the resolution -- said the President is "failing" in his responsibility to keep Americans safe.

"I think he has the highest responsibility of anybody in the country to combat the threat. No one has a greater responsibility to keep us safe than the President, by his actions and by his words, and certainly I would contend that he's failing in that responsibility," he said.

"We've always had Nazis. We always will," added Malinowski. "We've never had to question where the president of the United States stands on their way of thinking."

Rep. Debbie Mucarsel-Powell of Florida -- who, like Malinowski, is an immigrant -- especially pushed back on Trump's rhetoric about immigrants at the border.

"We are not invaders," she said. "Accepting refugees and asylum seekers does not pose an intrinsic threat to our way of life."

While the House passed a resolution last month broadly condemning discrimination against multiple groups, this one focuses on white supremacy and was inspired by the mosque attacks in New Zealand.

Trump has condemned the New Zealand attacks as "a horrible massacre" and "scenes of evil killing." When pressed further about the issue, he said he did not see a global rise of white supremacy and attributed recent attacks to a small group of people "with very, very serious problems."

The new resolution also calls for ramped-up funding at the Justice Department and the Department of Homeland Security for programs to combat domestic terrorism, and it urges social media companies to reevaluate policies that allow such rhetoric to go online.

The resolution is expected to first go through the House Judiciary Committee, which held a hearing Tuesday on the rise of hate crimes and white supremacy.

Clarification: This story has been updated to clarify the context of Trump's use of the word "animals" in 2018.