Walcott, who was making the rounds of radio and television news shows Wednesday morning, told WNBC-TV there were no talks scheduled.
"We're not negotiating. They want us to do something illegal. We can't do that at all. We're always open for communication ... It's not our responsibility and job to negotiate. They work for private companies."
Asked if the city planned to take the striking union to court, Bloomberg told Fox 5 New: "I don't think it's time to do that" and characterized the union's actions as illegal.
"How is it illegal to provide the most experienced drivers and matrons in the school buses?" Cordiello asked Tuesday.
The contracts expire June 30.
Associated Press writer Eileen AJ Connelly and Verena Dobnik contributed to this report.
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