Former Prime Minister Helen Clark imposed sanctions on Fiji Prime Minister Frank Bainimarama's regime after the 2006 coup.
Tomorrow, the Fijian leader will be asked to forgive and support her bid for the UN Secretary-General role.
Whether it is forthcoming could be a sign as to whether Mr Bainimarama agrees with Prime Minister John Key that the tension of the decade-long freeze in the relationship is "ancient history".
Mr Key will be the first Prime Minister to visit Fiji since the coup when he arrives today. He will meet with the Fijian leader tomorrow morning and said he would discuss Helen Clark's campaign.
New Zealand is supporting Fiji's bid for Peter Thomson, Fiji's Ambassador to the UN, to be the next President of the General Assembly and Mr Key said he was hoping Fiji would support Helen Clark.
"Frank [Bainimarama] may not be her No1 cheerleader, but I don't think he'll go out of his way to try to undermine her."
Although the Security Council rather than individual UN members select the Secretary-General, the support of other countries adds moral weight to a campaign.
Mr Key said Helen Clark had done the right thing in imposing those sanctions which applied to members of Mr Bainimarama's military regime for the eight years until elections were held in 2014.
"I think both sides have their own perspective on what took place and New Zealand will always defend the actions we took because we believe them to be right. We would be concerned to see the contagion effect of Fiji's coups and Fiji has had four. And I'm sure Frank [Bainimarama] and his team felt they did what they had to do."
His primary aim on the visit was to restore relations. However, he will be walking a tightrope as calls are made for him not to soft-peddle on democratic and human rights issues with Bainimarama.
There are hopes Cyclone Winston will be an icebreaker in the relationship after New Zealand sent a large deployment to help with the recovery.
Mr Key will visit a school the Defence Force rebuilt in Naiyala.
"If you look at the layers of political society, I think the political leadership at the very top is probably not that impressed with the actions Helen Clark and then our Government took during the time of the military coup. But every-day Fijians I think have always had a very warm relationship with New Zealand and our response to Cyclone Winston has just reaffirmed that emotional connection to New Zealand."
Mr Key will also try to resolve another hangover from the coup, after which Fiji was suspended from the Pacific Islands Forum. That suspension was lifted after Fiji's 2014 elections but Mr Bainimarama has boycotted it and is calling for New Zealand and Australia to be ejected before he will return. He has also tried to set up an alternative forum.
Mr Key said the Pacific Islands Forum was stronger with Fiji in it.
Mr Key has also undertaken to raise a ban Fiji has put on some New Zealand and Australian journalists.