A group of Boston public school parents launched a petition drive Friday to oust Superintendent ­Carol R. Johnson, arguing that she has lost the public’s trust after disclosure that she took no disciplinary action against a headmaster who admitted beating his wife and that she had sent a supportive letter to a judge presiding over the case.

The petition calls on Johnson, who apologized earlier this week for her actions, to resign immediately. If she does not, the signers ­demand that the School Committee fire her, saying Johnson “has shown a clear pattern of unwise, politically motivated, and uninformed choices that have put the children of Boston public schools at risk.”

“This is inexcusable and unforgivable,” said Valerie Madden, of Roxbury, whose children attend Boston Latin Academy and Mission Hill K-8 School, referring to Johnson’s failure to remove the headmaster, Rodney Peterson. “I do commend her for standing up and saying I’m sorry. But that’s not good enough. She has to go.”

Meanwhile, Johnson’s supporters are organizing a rally in support of the superintendent scheduled to be held Saturday morning at Bethel AME Church in Jamaica Plain. The rally is an opportunity for supporters to speak about all that Johnson has accomplished since becoming superintendent in 2007, said Rev. Ray Hammond, an ­organizer.

“Our concern is that the incident is being used as an opportunity for people to vent their anger against the superintendent for things she has done to advance the system,” said ­Hammond. “When you make tough choices, you are going to find people upset by it.”

However, Hammond added, “We concur this situation should have been handled differently. But we want to make sure [Johnson] continues to work to make Boston a better school system.”