Ruben Nunez, regional leader of the CNTE union, said the teachers started an "indefinite strike" to protest an eduction reform and "to boycott" the elections.
In the city of Oaxaca, the protestors broke into the state office of the electoral institute yesterday, causing damage in the main meeting room, burning papers and shoving personnel, an elections spokesman said.
Teachers drove a car into the door of the institute's local office in Juchitan before destroying furniture and setting a fire inside the facility, local police said.
National Electoral Institute president Lorenzo Cordova told reporters in Mexico City that the organization had closed most of its offices in Oaxaca in anticipation of trouble.
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Cordova said Oaxaca and the neighboring state of Guerrero are the areas "where we have had more problems to operate."
The CNTE's branch in Guerrero has also threatened to block elections there, along with Parents of 43 trainee teachers who were abducted by local police and allegedly killed by a drug gang.
Some 85.5 million Mexican will vote to elect 500 new federal congress lawmakers, nine governors and nearly 900 municipal leaders.