California Gov. Gavin Newsom renewed his push for state-level opportunity zone tax breaks with a revised proposal that loosens rules for affordable housing and green energy projects to qualify.

Newsom’s updated proposal—a modified version of federal opportunity zone tax breaks that allow investors to defer or reduce state tax on gains from investments in the zones—keeps the basic outlines of what he first released in May. In addition to limiting eligible projects to housing and green energy, the governor would still cap investments from specific funds at $100 million, cap total state allocations to $5 billion over the life...