California lawmakers overwhelmingly approved legislation that would create new restrictions for artificial intelligence, sending a bill that might set the national standard for regulating the new technology to the governor’s office for final consideration.

The State Assembly approved the legislation known as SB1047, which would require big A.I. systems to test their systems for safety before releasing them to the public. The bill also gives the state’s attorney general the power to sue A.I. makers for serious harms caused by their technologies, like death or property damage.

Gov. Gavin Newsom of California has not indicated his position on the legislation and has faced strong pressure from many in the tech industry to veto it. The proposed regulations have become embroiled in a fierce debate over how to regulate A.I., which, depending on whom you ask, has the potential for great benefits and harms to humanity.

“The Assembly has taken the truly historic step of working proactively to ensure an exciting new technology protects the public interest as it advances,” Senator Scott Wiener, co-author of the bill, said in a statement.

If the bill is signed into law, the state would become the standard-bearer of regulating a technology that has exploded in recent years, particularly with the introduction of humanlike chatbots and realistic image and video generators. Although the European Union has created the A.I. Act, no U.S. laws have been passed that restrict the use of riskier technology like facial recognition software.

The State Senate, which has already passed the bill, will vote again with new amendments this week in what is considered a procedural step. Mr. Newsom will then have until Sept. 30 to consider the bill, amid a flurry of lobbying by technology executives, venture capitalists, academics and federal lawmakers.