(CNN) -- Alabama's governor on Friday signed legislation that he said will "simplify and clarify" the state's controversial anti-illegal immigration law, considered one of the country's toughest.

Gov. Robert Bentley said in a press release that he approved the measure "to make House Bill 56 better," referring to the law that went into effect last year.

"There is substantial progress in this bill," the governor said. "Burdens on legal residents and businesses are eased, and the goal remains the same -- that if you live and work in Alabama, you must do so legally."

But critics have derided both the first bill and the revised version. Olivia Turner, executive director of the American Civil Liberties Union's Alabama branch, chided Bentley for authorizing the legislation and expressed hope that courts would strike it down.

"Governor Bentley had the opportunity to send a message to lawmakers that the racial profiling, discrimination and fear these laws spark must be stopped," Turner said in an e-mailed statement. "Sadly, he declined. We are hopeful the courts will soon overturn these shameful measures once and for all."

The original legislation, HB 56, included provisions requiring police who make lawful traffic stops or arrests to try to determine the immigration status of anyone they suspect might be in the country illegally.

A federal appeals court has blocked some components, however, including one requiring Alabama officials to check the immigration status of children in public schools. Bentley had called lawmakers in for a special session Thursday to consider, among a handful of other reasons, revising that law.

The new bill, HB 658, addresses some of its unintended consequences, including clarifying the types of documents that can serve as a form of official identification. But it does not address parts of the law that are at issue in federal courts. Among other changes, the new bill eases the most strict measures against subcontractors who unknowingly hire illegal immigrants.

It also contains language about exceptions for religious leaders, who had complained that their missionary work could be criminalized if the recipients of their aid were undocumented immigrants.

But Justin Cox, of the ACLU's Immigrant Rights Project, has characterized the related alterations as "just window-dressing."

HB 658 authorizes the use of state funds "to create a public database with the names of illegal immigrants," something Bentley says he does not support.

The governor noted, too, his "concerns" about the original law's provisions regarding education. Earlier this month, U.S. Assistant Attorney General Thomas Perez wrote a letter warning Alabama's education department that the law has had "lasting" and possibly illegal consequences for Hispanic school children.

"(The law has) diminished access to and quality of education for many of Alabama's Hispanic children, resulted in missed school days, chilled or prevented the participation of parents in their children's education, and transformed the climates of some schools into less safe and welcoming spaces for Hispanic children," Perez wrote.

Bentley on Friday downplayed the need to act immediately in this regard, given that this part of the law "is not currently in effect" due to a related legal action filed by the federal government. "We can re-address this issue if the need arises," he said.

"The bottom line is there are too many positive aspects of House Bill 658 for it to go unsigned," the governor said. "I don't want to lose the progress we have made. ... These changes make this a stronger bill."

Yet the Alabama Coalition for Immigrant Justice slammed Bentley for signing the revised legislation, despite his admitted reservations.

"In addition to his failure to show integrity and steadfastness in the face of extreme and hateful legislation, Governor Bentley also missed an opportunity to show leadership by asking the legislature to pause for a moment and let cooler heads prevail before committing the same mistake as they did last year when they shoved HB 56 into law," Zayne Smith, coordinator for the advocacy group, said in a statement.