The union's proposal was a counteroffer to BART's Sunday night contract proposal that included a 12 percent raise over four years.
On Tuesday afternoon, SEIU spokesman Des Patten praised the federal mediators who have joined the talks for bringing the two sides closer together.
"They're doing a good job," he said.
BART spokesman Rick Rice said progress has been made in the negotiations in the past 24 hours. However, he wouldn't say whether the transit agency is optimistic or not about reaching a settlement soon.
"We are working hard to get a contract," he said.
Meanwhile, AC Transit's board of directors asked Gov. Jerry Brown on Tuesday to invoke a 60-day cooling off period in their contract negotiations.