The Justice Department filed a lawsuit Wednesday against Texas over the state's implementation of a new immigration law allowing state and local law enforcement officials to arrest, jail and prosecute migrants who may have entered the U.S. illegally.

The Biden administration warned Texas that it would file a suit if Texas didn't assure federal officials by Wednesday that they wouldn't enforce the new state law, SB4. The state law also allows judges in Texas to issue de facto deportation orders. The Biden administration insists that immigration-related offenses are matters for the federal government, not states. 

"Texas cannot disregard the United States Constitution and settled Supreme Court precedent," said Principal Deputy Assistant Attorney General Brian M. Boynton, who heads up the Justice Department's Civil Division. "We have brought this action to ensure that Texas adheres to the framework adopted by Congress and the Constitution for regulation of immigration."  

Texas Attorney General Ken Paxton said in a statement Wednesday evening that "SB 4 was created to address the endless stream of illegal immigration facilitated by the Biden administration," and that he was "prepared to fight."

When the Biden administration threatened to sue Texas, Texas' Republican Gov. Greg Abbott said the Biden administration "not only refuses to enforce current U.S. immigration laws, they now want to stop Texas from enforcing laws against illegal immigration."

• Texas sheriff on enforcing SB4 immigration law: "It's going to be impossible"

The Texas law, which Abbott signed last month, comes as up to 10,000 migrants are crossing the southern border into the U.S. each day. 

Camilo Montoya-Galvez contributed to this report. 

Kathryn Watson is a politics reporter for CBS News Digital based in Washington, D.C.