Federal mediator George Cohen said late Tuesday progress has been made but has imposed a gag order on the parties.
The key issues have been salaries and worker contributions to their health and pension plans.
Talks began in April, three months before the June 30 contract expirations, but both sides were far apart. The unions initially asked for 23.2 percent in raises over three years. BART countered, offering a four-year contract with 1 percent raises contingent on the agency meeting economic goals.
The unions contended that members made $100 million in concessions when they agreed to a deal in 2009 as BART faced a $310 million deficit. And they said they wanted their members to get their share of a $125 million operating surplus produced through increased ridership.
But the transit agency countered that it needed to control costs to help pay for new rail cars and other improvements.
On Sunday, BART General Manager Grace Crunican presented a "last, best and final offer" that includes an annual 3 percent raise over four years and requires workers to contribute 4 percent toward their pension and 9.5 percent toward medical benefits.
The value of BART's proposal is $57 million, BART spokeswoman Alicia Trost said, adding that the agency is currently looking at ways to incorporate the unions' counterproposals into that cost.
SEIU Local 1021 executive director Pete Castelli said Monday the parties were somewhere between $6 million to $10 million apart.
Two unions, which represent more than 2,300 mechanics, custodians, station agents, train operators and clerical staff, now average about $71,000 in base salary and $11,000 in overtime annually, the transit agency said. BART workers currently pay $92 a month for health care and contribute nothing toward their pensions.
Meanwhile, workers at the Alameda-Contra Costa Transit District, a regional bus line, have threatened to strike on Thursday over their expired contract. On Tuesday, the AC Transit board requested that Brown impose a 60-day cooling off period, which a spokesman says the governor is considering.