The cost of the restoration, however, has also risen and is now at $127m, leaving a shortfall of $37m.
Matthews has agreed to take the new offer to the church's synod, made up of 225 clergy and elected members of the local diocese, in September.
"This not about favouring reinstatement over restoration or a contemporary new-build," Wagner said.
"It's about finding a way forward that doesn't leave everyone tied up in court for five to 10 years."
It's been more than six years since the Gothic-style 136-year-old cathedral was badly damaged in the 6.3-magnitude earthquake that devastated the Garden City on February 22, 2011.
Arguments over whether the building in the heart of Christchurch should be restored to its former glory, partly reinstated, or demolished and replaced with a modern new building have raged between the church, heritage campaigners, and the wider public ever since, and even reached the High Court.
Wagner said the Government offer is a significant amount of money, but it needed to balance the property rights of the church with the historical value of the building and the "need to break this deadlock".
"About half of Christchurch wants to see the cathedral reinstated, the other half wants a modernised version or a contemporary new-build, but really, everyone just needs a decision. It's time to move forward, and I think this is our best option," she said.
Mayor Lianne Dalziel says the council unanimously approved its grant on Friday, saying that the people of Christchurch wanted certainty and action about the cathedral.
"There was one message that dominated in the opinion poll commissioned by the Anglican Church about the future of the Cathedral. Make a decision now. People just want action," she said.
"This special grant is not in our long-term plan, so as soon as the synod has made its decision, we will institute a special consultative procedure, which will consider the grant and the terms under which such a grant would be made.
"Although such a grant can be seen as recognition of the Cathedral's heritage status and its important contribution to civic life and the Christchurch visitor experience, it is in fact the desire for certainty about the future of Cathedral Square and what it means for our city's recovery that drives my wish to see a final decision made that is not subject to litigation."
She added: "I'm hoping that the Council's proposed contribution will add weight to the Government's offer and at the same time show the synod that it is not just the fate of the Cathedral that lies in their hands - it's the ability for the city to flourish once more."
