Members of the union representing Boston school bus drivers rocked the city on Tuesday by deciding to go on a surprise strike that enraged Mayor Thomas Menino and disrupted the race for his successor.

Menino called the strike an “illegal action” and asked parents to have back-up plans ready for picking up their children. At a press conference outside the mayor’s office on Tuesday night, Marie St. Fleur, a Haitian-American who became a top Menino aide after serving in the state Legislature, urged the 635 bus drivers, many of whom are Haitian, to return to work.

City officials estimated that 33,000 students were affected by the strike, which may have cost as much as $35,000 in police overtime as officers helped some children to get to school. City officials and the company are pursuing legal action through an injunction that was not immediately granted on Tuesday night.

Students who were unable to make it into school that day were given excused absences.

With Acting Superintendent John McDonough, Police Commissioner Ed Davis, and School Committee chairman Michael O’Neill, standing behind him, an angry Menino called the union members “selfish people who want to cause disruption.”

Yesterday morning, the union members were back in their driver’s seats, but it was unclear whether or not there would be afternoon bus serve and what the rest of the week would bring.

The bus drivers have been in talks with Veolia Transportation, the management company that has a contract with the city. They told WHDH-Channel 7 that they have complained about driving schedules that were too difficult to execute and didn’t leave enough time for things like bathroom breaks. They have also voiced displeasure with the company placing a GPS (global positioning system) on the buses and using it for evaluations and tracking buses.

The United Steelworkers District 4, which has the bus drivers’ union under its umbrella, blasted the strike and demanded they return to work.

The two mayoral candidates, state Rep. Marty Walsh and City Councillor At-Large John Connolly, also ripped into the bus drivers for abandoning the buses on Tuesday morning. Walsh, a top labor leader, called on them to return to work; Connolly said the drivers should face consequences for the disruption.

“The actions of the school bus drivers’ union were outrageous, unlawful, and put the safety of our children at risk. It’s unconscionable what was done this morning and is emblematic of a deeper problem where we do not put our children first when we think about making our Boston public school work,” Connolly said, according to the State House News Service.

Walsh, in Egleston Square for an endorsement announcement, said the bus drivers were violating their contract.

Material from State House News Service was used in this report.