SACRAMENTO, Calif. — California Gov. Jerry Brown said Friday that he has vetoed legislation allowing employees of some small businesses to take up to six weeks of leave to bond with a new child without losing their job or health insurance.

Under the measure aimed at businesses with 20 to 49 employees, workers with at least a year on the job would have been eligible for the benefit beginning Jan. 1, 2018.

Businesses wouldn’t have been required to pay the worker. Democratic Sen. Hannah-Beth Jackson of Santa Barbara, the author of the bill, said employees could apply to a state program to receive partial wages.

Brown said he was concerned it would harm small firms.

“It goes without saying that allowing new parents to bond with a child is very important … I am concerned, however, about the impact of this leave particularly on small businesses and the potential liability that could result,” Brown, a Democrat, wrote in a veto message to lawmakers.

The California Chamber of Commerce and other business groups had urged him to veto it, saying the measure could create staffing shortages that hurt business operations.

The legislation, SB654, would have expanded an existing state law that applies to firms with 50 or more workers.

California once was a leader on family leave, but over the past decade has slipped behind nine other states that require it for smaller businesses, Jackson has said.

Her bill would apply to 2.7 million more Californians than the current parental leave law while affecting 6 percent more businesses, she said.

Those employees already pay into the state’s Paid Family Leave Program, but many don’t take advantage of it because they can’t get the time off work.

Jackson said in a statement that she was disappointed in the veto and would work to advance the issue in the future. “As many states move forward with strong policies for parental leave, California cannot afford to be left behind,” she said.

Brown suggested allowing workers and employers to pursue mediation before a lawsuit is filed “is a viable option that should be explored.”