OAKLAND, Calif.—A proposal that could make this city a gateway for Utah coal to be shipped overseas has become a political flash point and put pressure on Gov. Jerry Brown, a former mayor known for his warnings on climate change, to come out against the project.

The proposed deal would grant four coal-producing counties in Utah rail access to a major commodities shipping terminal under development on city land, adjacent to the Port of Oakland, in exchange for a $53 million investment. City officials hope the redevelopment plan, on an old Army base, would bring thousands of jobs to a city that still has pockets of poverty and violence even as the region’s tech sector booms and housing costs rise.

California ports in Stockton, Richmond and Long Beach export coal, but because of climate change and pollution concerns, such terminals have become highly contested on the West Coast. Environmentalists, who have defeated similar proposals in Oregon and Washington, have filed suit against the city, the project and developers. They are now calling on Mr. Brown, a Democrat, to speak out forcefully against coal being shipped through his former city.

“We are hopeful that he won’t let his hometown of Oakland become a thoroughfare for dirty coal,” said Jessica Dervin-Ackerman, conservation manager with the local chapter of the Sierra Club.

Mr. Brown declined to comment on the Oakland terminal. While he has sounded an alarm on climate change—recently telling a Vatican symposium that 90% of the world’s coal must remain unused to evade the perils of global warming—as governor he has angered environmentalists by allowing the expansion of hydraulic fracturing in the state.