The union's president has said the group has nothing to do with any sick-outs. Union officials weren't immediately available for comment Wednesday.
Meanwhile, buses and trains were operating at about 70 percent of their normal service Wednesday, up from 50 percent a day earlier and from 33 percent on Monday, agency spokesman Paul Rose said. There was even a slight possibility that the popular cable cars could also resume service in the afternoon, he added.
"The fact that we have more vehicles on the street than the last two days leaves us cautiously optimistic," he said.
The agency and its workers are at odds over a new contract. Workers overwhelmingly rejected a contract proposal on Friday that union officials said would have resulted in a pay cut.
The union's president, Eric Williams, said Tuesday that the labor group has nothing to do with the sick calls and urged those who called in sick to be prepared to have a doctor's note.
The agency known as Muni runs buses, light rail and street cars in addition to the cable cars and serves about 700,000 passengers each day. Its operators, represented by Transport Workers Union Local 250-A, rejected the contract by a 1,198-42 vote Friday, according to totals on the union's website.
The workers are not allowed to go on strike, but they can call in sick.
Transit officials said those who reported being sick must confirm they were ill to get sick pay and could be subject to discipline up to being fired.
The contract that Muni workers rejected would have given them a raise of more than 11 percent over two years. However, it also would have required them to cover a 7.5 percent pension payment currently paid by the transit agency, said Rose, the agency spokesman.
The contract would have increased operator pay to $32 an hour, making them the second highest-paid transit workers in the country, Rose said.
Williams said other city workers were getting a better pension deal than Muni drivers. "Our members are hard-working, and all we want is fairness," he said.