Feinstein, who is up for reelection in November and is facing a challenge from the left, indicated last week that she would introduce the legislation. In addition to Feinstein, more than 30 Democratic senators have signed on to the bill.

Feinstein added on Friday that she hoped Republicans would support the legislation and "put an end to this immoral policy.”

Democrats and outside groups have slammed the Trump administration over its immigration policies. Democrats argue that, in particular, prosecuting individuals trying to seek asylum may violate U.S. obligations under international law.

The fight comes as the Department of Homeland Security is for the first time prosecuting people who are caught crossing the border illegally, a crime that’s been on the books since 1986.

The Trump administration is trying to shift the blame to Democrats, arguing they are to blame for creating "loopholes" that leave border authorities no choice but to separate children from parents who are facing criminal charges.

"Separating families at the Border is the fault of bad legislation passed by the Democrats. Border Security laws should be changed but the Dems can’t get their act together! Started the Wall," Trump said in a tweet this week.

Sessions announced a "zero tolerance" policy earlier this year for immigrants illegally crossing the Southwest border.

"If you cross the border unlawfully, then we will prosecute you. It’s that simple,” Sessions said last month at a press conference at the U.S.-Mexico border near San Diego. “If you are smuggling a child, then we will prosecute you. And that child may be separated from you, as required by law."

He added in a statement: “To those who wish to challenge the Trump Administration’s commitment to public safety, national security, and the rule of law, I warn you: illegally entering this country will not be rewarded, but will instead be met with the full prosecutorial powers of the Department of Justice.”