A federal appeals court on Tuesday continued to temporarily bar Texas from enacting a sweeping and controversial new immigration law while further appeals litigation plays out.

The state's Senate Bill 4, also known as SB4, would allow Texas authorities to arrest anyone suspected of being an unauthorized migrant and order them to leave the U.S. or face prison time, law enforcement action that is typically carried out by federal agents.

The law would also give judges the power to order migrants to be transported to a port of entry and returned to Mexico regardless of their country of origin.

The U.S. 5th Circuit Court of Appeals panel, in a 2-1 decision, ruled on Tuesday that "Texas has not shown that it is likely to succeed on the merits of plaintiffs' preemption claims. There is considerable authority supporting that the core provisions of S. B. 4 are field, or alternatively, conflict preempted by federal law."

The 5th Circuit has scheduled oral arguments on April 3 to further hear the case.

The circuit's chief judge, Priscilla Richman, wrote in the majority opinion that based on precedent, Texas is likely to lose at the U.S. Supreme Court because "for nearly 150 years, the Supreme Court has held that the power to control immigration—the entry, admission, and removal of noncitizens—is exclusively a federal power."

Advocates, including attorneys with the American Civil Liberties Union, who oppose SB4, lauded the decision.

"This unconstitutional proposal should never have gotten this far, and we look forward to the courts blocking it permanently so we can get back to discussing real policy solutions," said Edna Yang with American Gateways.

The 5th Circuit panel had heard oral arguments last week about whether to temporarily block the state of Texas from moving forward with SB4.

The legislation has been cheered on by conservatives and Gov. Greg Abbott, a Republican, calls SB4 necessary to address the White House's "dangerous" border policies. But the Biden administration has warned that it will "throw immigration enforcement into chaos" and blatantly conflict with the constitutional authority of federal immigration authorities.

Some local authorities say they do not have enough resources to fully enforce the law and have no plans to make it a priority.

Texas Solicitor General Aaron Lloyd Nielson said in a hearing on a March 20 before the 5th Circuit that Texas has a right to defend itself and the federal government should not get in the way.

"Texas has decided that we are at the epicenter of this crisis -- we are on the front line -- and we are going to do something about it," Nielson told the court then.

He argued that the SB4 effectively "mirrors" federal law by outlawing illegal border crossings on a state level.

Department of Justice Attorney Daniel Tenny argued to the court that the responsibilities of enforcing immigration law are exclusively a federal responsibility and that Texas is interfering with deportation processes.

"There are plenty of things that a state can do that would affect the problems that Texas is complaining about," Tenny said.

It remains unclear how certain provisions of the law would interact with federal enforcement. For example, the court questioned Nielson on March 20 about what would happen if a migrant was delivered to a port of entry and then re-released by Border Patrol.

"This is uncharted because we don't have any cases on it," Nielson said. But he said that he believes such migrants could be re-arrested by the state under SB4.

Judge Richman, a George W. Bush appointee, several times voiced skepticism of Texas' claims in last week's hearing. "This is the first time, it seems to me, that a state has claimed it has the right to remove illegal aliens," she said. "This is not something that has historically been exercised by states, right?"

Judge Andrew Oldham -- a Donald Trump appointee, former general counsel to Gov. Abbott and former deputy solicitor general of Texas -- was the most sympathetic to the state.

The panel's third judge, Joe Biden appointee Irma Ramirez, also the first Latina to serve on the 5th Circuit, did not ask any questions during the argument.

Whatever the appeals court ultimately decides will almost certainly end up back at the U.S. Supreme Court, which has not weighed in on the merits of the state law.

ABC News' Armando Garcia, James Scholz and Mireya Villarreal contributed to this report.