The city’s Department of Education will increase funds and tighten regulations for translation services for parents, as part of an agreement to resolve a running dispute between the City Council and Mayor Michael R. Bloomberg. The agreement will be announced today, according to Make the Road by Walking, an immigrant advocacy group that took part in the negotiations. The new services are an attempt to address a dispute over the Education Equity Act passed by the Council, which required the department to provide interpretation services at large meetings at which at least 10 percent of those likely to attend would be unable to speak English. Another requirement was that documents intended for parents, like report cards and important notices, had to be available in the nine languages most widely used in the city. The Council passed the act in December, on a 35-to-11 vote, but the mayor vetoed the measure in January, saying that, though he agreed with the substance of the proposal, only the state government could legislate on education matters. The agreement will have many of the same features as the Education Equity Act.