ALBANY, N.Y. — The state has a new law to stop independent political groups from unfairly helping candidates for elected office, though critics say it won’t fix chronic corruption in Albany and could have negative unintended consequences.

Democratic Gov. Andrew Cuomo signed the law on Wednesday, calling it a “first-in-the-nation” response to the U.S. Supreme Court’s Citizens United ruling, which prohibits restrictions on independent political spending. Critics say the ruling allows wealthy donors or organizations to use independent groups to avoid campaign finance limits when supporting candidates.

“New York is taking aggressive action to restore the people’s faith in government and increase accountability and transparency in the electoral process,” Cuomo said. “This new legislation will root out bad actors and shine a spotlight on the sordid influence of dark money in politics.”

The law will require charitable nonprofits to identify donors who give $2,500 or more, a move the New York Civil Liberties Union worries will discourage people from contributing to groups involved in controversial advocacy, such as Planned Parenthood or gun rights groups, for fear they would be publicly identified.

Many good-government groups are subject to the new rule, meaning they will have to disclose the identities of donors.

“While the intention of the bill is to bring transparency to dark money in politics, it is overbroad,” said Robert Perry, legislative director for the New York Civil Liberties Union.

Other critics say the law largely ignores the causes of a wave of corruption that has seen more than 30 lawmakers leave office facing allegations of corruption or misconduct since 2000. They want to lower the state’s notoriously high campaign contribution limits, particularly a loophole that allows limited liability companies to make almost unlimited contributions without disclosing their donors.

Susan Lerner, executive director at Common Cause New York, said her organization was “deeply disappointed” in the bill, which originated with Cuomo. Common Cause, which says it’s dedicated to restoring the core values of American democracy, joined four other organizations in a letter to Cuomo urging him to veto the bill.

“Common Cause New York supports efficient, meaningful transparency laws that advance the public interest, but this law fails to meet that standard,” she said.

A Cuomo spokeswoman dismissed the complaint.

“Everyone is all for transparency, except when it comes to them,” spokeswoman Dani Lever said. “We are just surprised to learn that applies to self-appointed good-government groups, too.”