Gavin Newsom dived into the highly charged debate over prescription drug prices in his first week as California’s governor, vowing action on a topic that has enraged the public but has proved resistant to easy fixes.

His idea: Find strength in numbers. Within hours of taking office on Monday, Mr. Newsom signed an executive order proposing a plan that would allow California to directly negotiate with drug manufacturers.

The state would bring to the bargaining table not just the 13 million beneficiaries of Medi-Cal (California’s version of Medicaid), but also other state agencies that purchase drugs, including coverage for state workers and prisoners. Down the road, the plan could possibly allow private insurers and employers to join in the savings.

“We think this is a significant step forward,” Mr. Newsom said in a video address. “It’s the right thing to do, and I recognize deeply the anxiety so many of you feel around the issues related to the cost of prescription drugs, and I hope California’s efforts here can lead the way for other states to consider the same.”