The constitution includes a clause giving immunity to all of those involved in past coups.
Those covered include interim Prime Minister Frank Bainimarama, ministers, public servants, courts, military and police.
The immunity will not be able to be revoked by future governments.
Mr Key told the Herald the constitutional pardon was a compromise which could be necessary to guarantee that Fiji held fair and democratic elections next year.
"Practically, I don't think there's any way you're going to get a constitution and elections held without it. It's a kind of price for taking the next step.
"It's not a deal breaker from our point of view. We might not like it but it's not a deal breaker."
At the four-day forum, New Zealand would discuss support for Fijian elections. This was likely to come in the form of funding, security and observers.
Mr Key said he was highly optimistic the long-delayed elections would be held, probably next September.
"I might be proven to be wrong, but I'd be way more than 50/50 that they'll hold those elections. In the end, this is a country which has been beset by a coup culture and we hope that we've closed that chapter."
New Zealand's stance towards Fiji continues to soften, in particular with regard to travel sanctions such as those on on Fijian sports players.
"Increasingly we are issuing more waivers. Is that a softening of the stance? I suppose that's true."
Australian Foreign Minister Bob Carr also said the draft constitution was an important step towards democratic elections.
University of Auckland senior lecturer in Pacific studies Steven Ratuva said the constitution was a "quite liberal" document for a military-backed regime. But he was concerned that the immunity clause could protect future coup leaders as well.
Fijians 'locked out' of democracy plan
Fijians have been "locked out" of the country's plan for democracy, locals say, with no way to hold past coup leaders to account.
Fiji National Council of Women general secretary Fay Volatabu, speaking to the Herald from Suva, said many of the key provisions in an independently drafted constitution had been removed by the military-led Government. These omissions included a requirement for all political parties to allocate 30 per cent of their electorate seats to women - an attempt to transform the male-dominated Government.
Ms Volatabu was also concerned about the immunity clause.
The constitution replaced a draft version drawn up by an independent commission, which was thrown out by the coup leaders in January. The original document was based on 7000 public submissions, while the second had just 126 submissions and was led by Government.
Fiji's draft constitution
*Outlaws further coups.
*Creates 50-person Parliament with a single constituency, instead of four constituencies, and elections every four years.
*Includes comprehensive bill of rights and clauses on free speech.
*Grants immunity to past coup leaders and says this clause can never be repealed.
*Can be amended only by law supported by 75 per cent of MPs and 75 per cent of voters.
