The legislation would also undo Trump's crackdown on so-called "sanctuary cities," which don't follow federal immigration law.
Homeland Security Secretary John Kelly defended the arrests earlier this week, noting that roughly 75 percent of the 680 undocumented immigrants arrested were "criminal aliens."
Under the new order, the Trump administration expanded the definition of “criminal alien” to include individuals who entered the country without authorization, which was originally considered a misdemeanor offense.
Immigrants who have "committed acts that constitute a chargeable criminal offense" are now priorities under the order, even if they have not yet been convicted.
Top Democrats and outside groups have decried the recent string of raids, arguing they are sparking fear in the Hispanic community.
Durbin argued on Thursday that the change threatens millions of undocumented immigrants currently in the country.
"[They] are currently living in the United States with no threat to our country, no criminal record, with strong families," he said.
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It’s the first bill newly elected Nevadan Cortez Masto has sponsored.
Reports emerged over the weekend that ICE officials had conducted raids in several cities, though an exact number of arrests was not disclosed. The Department of Homeland Security said the operations were "consistent with the routine, targeted arrests carried out by" immigration enforcement teams "on a daily basis."
Trump took a hard line on immigration during his presidential campaign pledging to deport roughly 11 million undocumented immigrants.
But he appeared to soften that stance more recently, saying he would reach a "deal" on undocumented immigrants brought into the country as children and focus on immigrants with criminal records.
He also defended his policies during a joint press conference with Canadian Prime Minister Justin Trudeau this week, pledging he would step up his effort to deport "criminal" aliens.
“I said we will get the criminals out — the drug lords, the gang members — we're getting them out,” Trump said.