SAN FRANCISCO — Gov. Gavin Newsom says he has concerns about enacting tougher rules that limit doctors from granting medical exemptions for children's vaccinations.

The measure would give state public health officials instead of local doctors the authority to decide which children can skip their shots before attending school. It's being considered by the state Assembly amid growing cases of measles.

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Newsom told reporters at the California Democratic Party Convention Saturday that although he supports immunization, he has concerns about having government officials sign off on vaccine exemptions. He said as a parent, he wouldn't want a bureaucrat to make a personal decision for his family.

California does not allow exemptions based on personal beliefs, but still allows exemptions for children who must avoid vaccinations for medical reasons.

WATCH MORE: Senate Bill 276 would let state decide who can get a vaccine exemption

Currently, parents can file a doctor statement that explains how an immunization puts a child at risk. Then that child is exempt from getting the vaccine or vaccines. Senate Bill 276 would change all of that.