The contemporary structure would be the cheapest and quickest to build, taking between four and nine years, and costing between $56 million and $74 million.
Restore Christ Church Cathedral group spokesperson Mark Belton welcomed the options, saying the important thing is the church has acknowledged the building can be saved.
"We are thrilled - it is very important the church has put forward an option that includes full restoration."
Mr Belton doubted the figure put forward by the church, saying other estimates place the cost between $90m-$120m.
He said people should not balk at the cost, as it is less than restoration projects at the Arts Centre and Provincial Chambers, and less than the proposed central city stadium or convention centre.
"Great buildings don't come cheap, particularly cathedrals."
Mr Belton said engineers had already done work for the group pro-bono and he expected this to continue. There had also been offers of donations from New Zealanders and from overseas should the decision be made to restore the church.
He also argued the building would not take 22 years to rebuild, instead it would take closer to 10 years.
"We shouldn't forget the original took 40 years to complete."
Mr Belton said the other options were "quite irrelevant".
"They are just not needed now we have the restoration option [on the table] - they are just distractions."
He said restoration was the "least contentious" option and would be a "healing project for the Christchurch community".
However Bishop Victoria Matthews has hinted she is in favour of the option of a new contemporary cathedral.
In an opinion piece in The Press today, she wrote: "I want our Cathedral to inspire and to uplift. I believe we all want a safe Cathedral so no matter what the earth delivers, in the future the Cathedral can embody 'sanctuary' for the city. And the Cathedral needs to encourage the mission of God across the region and beyond.
"This means having a new Cathedral in the Square in a reasonable time frame and a beautiful building that will not cost so much that the Cathedral is built at the expense of ministry to and by the people."
Those opposing the demolition of the cathedral said it was too early for Anglican church officials to release their own proposals while court action determining the fate of the building was continuing
A Court of Appeal hearing is expected to take place in a couple of weeks.
The Great Christchurch Buildings Trust took the neo-Gothic style cathedral's owner, the Church Property Trust, to court in October in a last-ditch legal bid to have it repaired.
The cathedral was badly damaged in the February 22, 2011 quake, which snapped its spire.
Its damaged state prompted the Canterbury Earthquake Recovery Authority to issue a section 38 unsafe building notice, which demanded urgent action.
Two public forums will be held this month, and views on the designs will be sought until early May when Church Property Trustees will select their preferred option.
More: Official website