LOS ANGELES  A ballot measure to make California the first state to legalize the sale and use of marijuana has won the support of one of the state’s most powerful union, officials said Monday, offering the proposition a shot of mainstream legitimacy as well as a potential financial and organizational lift.

The decision by the executive board of the Service Employees International Union of California will be announced in the next few days, according to officials who have been briefed about it but were not allowed to speak publicly before it was announced.

The measure has faced strong opposition from law enforcement groups, including Sheriff Lee Baca of Los Angeles County, who said he would lead a campaign against it as a threat to public safety.

But the proposal also won support on Monday from some former law enforcement officials, including police officers, judges and prosecutors.