The ruling General Synod, meeting in York, debated a report about abuse in the Chichester Diocese.
Members unanimously backed an earlier apology issued by the Archbishops of Canterbury and York.
Meanwhile, a man was arrested after two stewards were allegedly attacked at a Synod service in York Minster.
A Church of England spokesman said a man entered the minster as the service was starting and attacked the stewards when they asked him to stop.
He was restrained as members of the congregation and senior members of the church, including the Archbishop of Canterbury, looked on.
A member of the Archbishop of York's staff and a steward suffered minor injuries.
The Archbishop of Canterbury, the Most Reverend Justin Welby, told the Synod child abuse debate there had to be "a complete change of culture and behaviour" in the Church.
"And, in addition, there is a profound theological point," he added.
"We are not doing all this, we are not seeking to say how devastatingly, appallingly, atrociously sorry we are for the great failure there has been for our own sakes - for our own flourishings, for the protection of the Church - but we are doing it because we are called to live in the justice of God and we will each answer to him for our failings in these areas."