LOS ANGELES — Breaking with Democrats in the State Legislature, Gov. Jerry Brown vetoed a bill on Monday that would have made California the first state to allow immigrants who are not citizens to serve on juries, saying that the responsibility should come only with citizenship.

As leader of a state with 3.5 million noncitizens who are legal permanent residents, Mr. Brown in recent weeks had signed into law numerous measures that put California at the vanguard of expanding immigrant rights, including granting driver’s licenses to illegal immigrants.

On Saturday, he signed several such bills, most prominently legislation stopping local law officers from detaining immigrants and transferring them to federal authorities unless they have committed certain serious crimes. And he agreed in August to let noncitizens monitor polls for elections.

But the governor drew the line at allowing legal immigrants to serve on juries. “Jury service, like voting, is quintessentially a prerogative and responsibility of citizenship,” Mr. Brown said in a brief veto message. “This bill would permit lawful permanent residents who are not citizens to serve on a jury. I don’t think that’s right.”