More than half the 85 honours recipients offered the option of becoming knights or dames say they want the titles.
Prime Minister John Key yesterday said 53 responses had been received - 46 accepting the titles and seven rejecting them.
The rest have until the end of June to decide.
Mr Key said he did not know the names of those who had decided, but a list would eventually be published.
One of those accepting the reinstated title 'Sir' is Maori leader Harawira Gardiner, founding head of the Waitangi Tribunal and former head of Te Puni Kokiri, the Ministry of Maori Development.
He was made a Distinguished Companion of the New Zealand Order of Merit for his services to Maori, last June.
Last night, he told the Herald that although he had not officially accepted the honour, he would do so.
"I think it's not mine to turn down. A lot of people have worked hard alongside me and this is a recognition of that," he said.
The titles "dame" and "sir" were restored to the honours system last month after being dropped by the previous government in 2000.
Rugby great Colin Meads last night said he had not accepted the title - "yet".
Business leader Eion Edgar said he had accepted the title of Sir - a decision that had been made easier by a push from friends, family and the wider community.
"The day after it was announced I was a recipient, I must have got more than 80 texts, emails and calls saying: 'Please accept'," Mr Edgar said.
Winemaker George Fistonich a said that after talks with family and colleagues, he decided accepting the title would be a good thing.
"We thought it was good for the wine industry and also for our family, to accept it, so I have," Mr Fistonich said.
Air Marshal Bruce Ferguson and former Tatua dairy co-op chairman Dr Alan Frampton said they had been told not to reveal their decisions.
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