Sen. Ruben Gallego, D-Ariz., who was sworn into office last week, said he supports the Laken Riley Act.
The bill, which would require ICE to take custody of illegal migrants who commit theft-related crime and was named after the Georgia nursing student who was murdered by an illegal migrant, recently passed the House.
"Arizonans know the real-life consequences of today's border crisis," Gallego said in a statement. "We must give law enforcement the means to take action when illegal immigrants break the law, to prevent situations like what occurred to Laken Riley. I will continue to fight for the safety of Arizonans by pushing for comprehensive immigration reform and increased border security."
Gallego supported the bill last year when it passed the House, though it was never voted on in the then-Democrat controlled Senate.
Critics of the bill say it does nothing to secure the border or provide sensible immigration policy.
"Instead [it] gives state governments unprecedented authority to use the courts to overturn small and large decisions made by the federal government on immigration and foreign policy," said Nayna Gupta, policy director at the American Immigration Council to The Hill.
The House on Tuesday approved the bill 264-159, with 48 Democrats joining all Republicans in support. It will head to a vote in the Senate on Friday.
All 52 Senate Republicans are co-sponsoring the reintroduced bill, as is Sen. John Fetterman, D-Pa., meaning Republicans need the support of seven more Senate Democrats to reach the 60 votes required to overcome a filibuster.
The legislation grants power to attorneys general to sue the federal government if they can show their states are being harmed by the failure to implement national immigration policies, according to CBS News.
Riley's murderer had been arrested for shoplifting the week before he killed her, but he had not been kept in jail, NBC News reported.