SAN ANTONIO, Texas (NewsNation) — Despite a Supreme Court extension blocking the law, Texas border sheriffs have informed NewsNation that they’re ready to enforce a new state law granting state and local law enforcement the authority to arrest people suspected of illegally crossing the Texas-Mexico border.

“I don’t see myself doing anything different than I already do,” said Terrell County Sheriff Thaddeus C. Cleveland. “What I mean by that is once I apprehend people I suspect of being here in the city illegally, I get in touch with the Border Patrol, and they come out. They take possession of them.”

“It’ll benefit, especially those that are along the border,” said Brooks County Sheriff Benny Martinez. “A lot of these issues that are surfacing are on those that really don’t have the concept as to what we go through on a daily basis down here. We’re not trying to target anything, but it is illegal to come between the port of entries for sure.”

The extension grants the court additional time to consider what opponents have labeled the most extreme state attempt to regulate immigration since a 2012 Arizona law the Supreme Court partially invalidated.

Justice Samuel Alito opted Tuesday to extend the suspension of the controversial law, known as Senate Bill 4, which would represent one of the strictest state immigration laws in U.S. history.

If SCOTUS hadn’t intervened, the law would have taken effect Wednesday.

Alito’s order is set to expire Monday, but he or the full Supreme Court could take further action before then. Alito handles certain emergency matters involving cases from a group of states including Texas.

If SB4 is implemented, it will authorize law enforcement officers to inquire about people’s immigration status during routine stops and make arrests.

Just days ago, numerous organizations gathered for a rally outside the state capitol in Austin, urging Gov. Greg Abbott to stop SB4 along with Operation Lone Star, which through a multiagency effort has led to more than 503,800 arrests of immigrants in the country illegally.

Following the Supreme Court’s extension of the freeze, a border organization named LUPE filed a lawsuit to block the legislation, alleging it promotes racial profiling, KRGV-TV reported.