(CNN) -- Alabama's governor on Thursday called in lawmakers for a special session in part to further explore changes to the state's anti-illegal immigration law, considered the country's toughest.
The day before, lawmakers had passed a bill, HB 658, which proposed changes to the state immigration law, which is currently being challenged in federal court.
Rather than sign it into law or veto it, Gov. Robert Bentley summoned lawmakers to take up the bill one more time.
Supporters of HB 658 said the changes would make the law better, but critics quickly pounced on it, saying it would make it even worse.
The new bill addresses unintended consequences of the state's immigration law, including clarifying the types of documents that can serve as a form of official identification, but does not address parts of the law that are at issue in federal courts.
Bentley wants to "have an opportunity to further clarify the law," a news release from his office said.
As passed by the state House and Senate, HB 658 appears to be an attempt to mollify some of the bill's critics.
But it fell short, said Justin Cox of the ACLU's Immigrant Rights Project.
Religious leaders complained that their missionary work could be criminalized if the recipients of their aid were undocumented immigrants, and one version of the new bill included an exception for this. But the final bill barely had anything resembling an exception, Cox said.
"I think it was just window-dressing," he said.
The new bill also eased the most strict measures against subcontractors who unknowingly hire illegal immigrants.
Critics, including the American Civil Liberties Union, said the biggest problem of the new bill was the requirement that the Alabama Department of Homeland Security post online the names of illegal immigrants that appear in state courts.
The ACLU criticized the new bill for not tackling any of the most contentious parts of the law whose constitutionality is being challenged.
Bentley's call for further discussion on the law cites his desire to see some of the controversial parts of the law modified.
One portion of the law that is currently enjoined calls for schools to collect information on the immigration status of their students.
"Governor Bentley believes that revising this section to prevent children from being interrogated would allow the injunction to be lifted, making the law more effective," the statement said.
The governor also cautioned against the provision requiring the online posting of court records of undocumented immigrants, something critics have called the "Scarlet Letter provision."
"Such a list could be counterproductive and take away from the focus of the original law," the governor's new release said. "The purpose of this particular section of the law is to gather data and statistics, not names."
"The essence of the law must remain the same, and that is if you live or work in Alabama, you must do so legally," Bentley said. "We must make sure that final revisions to the immigration law make the law more effective, help promote economic growth, ensure fairness, and provide greater clarity on the application of the law. I believe these additional revisions will help us as we accomplish those goals. A more effective, enforceable bill is a stronger bill."
During the special session on Thursday, Alabama lawmakers introduced two new immigration bills, one in the House and one in the Senate. The text of the bills appeared to be largely identical to HB 658.
The bills were not debated, and no debate on them has been scheduled, said Scott Tracy, a spokesman for Alabama House Speaker Mike Hubbard.
Jeremy King, a spokesman for Bentley, said Thursday night that the legislators would set a calendar detailing when issues come up in the session.
"The governor has been involved for months on various issues including the revisions to the bill. We think there are opportunities to further clarify and simplify the immigration law and make it more effective," King said. "We have a good working relationship with the legislators, and we are ready to work with them during this special session to see that these issues are addressed."
CNN's Joe Sutton and Catherine E. Shoichet contributed to this report.