The announcement came Friday, as union leaders were warning commuters that they were prepared to strike and shut down one of the nation's largest rail systems for the second time this summer if they don't reach an agreement on a new contract this weekend.
San Francisco's Superior Court has agreed to open its Civic Center courthouse on Sunday if necessary to hold a hearing on Brown' request for an injunction.
Bay Area Rapid Transit managers and union leaders were negotiating Friday, but their proposals remained tens of millions of dollars apart on wages, pensions and health care benefits.
Officials with the San Francisco Chamber of Commerce had complained earlier Friday that state and local elected officials weren't doing enough to resolve the labor dispute and stop workers from striking. The business group is calling for state legislation to prevent future BART strikes.
California Sens. Dianne Feinstein and Barbara Boxer sent a letter to BART managers and union leaders Thursday, urging them to "resume negotiations in good faith, end the dispute, and work together to avoid any further disruptions to BART service."
Brown's decision to empanel the board of inquiry prevented a strike from beginning last Monday.
The labor dispute previously resulted in a 4 1/2-day strike in early July that snarled traffic on roadways and left commuters facing long lines for buses and ferries.
BART is the nation's fifth largest rail system, carrying an estimated 400,000 daily riders from the farthest reaches of San Francisco's densely populated eastern suburbs to San Francisco International Airport across the bay.