Gov. Gavin Newsom threw cold water Saturday on state legislation that would tighten California’s rules on providing medical exemptions for childhood vaccinations.

“I like doctor-patient relationships. Bureaucratic relationships are more challenging for me,” Newsom told reporters at the California Democratic Party convention in San Francisco. “I’m a parent. I don’t want someone that the governor appointed to make a decision for my family.”

Sen. Richard Pan, D-Sacramento, has proposed a bill that would require the state Department of Public Health to approve every request for a medical exemption to a child’s immunization schedule.

Newsom did not explicitly say he would veto the bill, SB276, which passed the state Senate last month and moves now to the Assembly. But he cast serious doubts on its prospects should it reach his desk.

“With respect, as a father of four that goes through this on a consistent basis, that’s just something we need to pause and think about,” Newsom said.

A measure that Pan carried in 2015 eliminated California’s personal-belief exemption that parents could claim to excuse their children from shots for measles, chicken pox, whooping cough and other infectious diseases. Children without a medical exemption must be fully vaccinated to attend public or private schools. California is one of three states where that is the case.

Pan contends that more oversight is necessary because unscrupulous doctors are providing bogus medical exemptions, putting some schools at risk of spreading contagious disease because not enough students are vaccinated to provide “community immunity.” Opponents of his bill, who have descended on the Capitol by the thousands, argue that the government should not be involved in a decision best left to families and their doctors.

Newsom said he was a “strong supporter” of the 2015 vaccine law. He also rejected any notion that he was “parroting that mantra” from anti-vaccine skeptics who believe immunizations are linked to autism and other health problems.

“I believe in immunizations. I do not subscribe to their point of view broadly,” he said. “However, I do legitimately have concerns about a bureaucrat making a decision that is very personal.”

Alexei Koseff is a San Francisco Chronicle staff writer. Email: akoseff@sfchronicle.com Twitter: @akoseff