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Jackson was notified of the fire, which destroyed the homestead at Paradise, about 20km past the Glenorchy township, by the Paradise Trust which operated the property.
Picturesque at every turn, the area was showcased in the Lord of the Rings trilogy, which Sir Peter directed.
After learning of the May 23 fire, he sent a note to the trust through his agent.
''We first came to Paradise over 15 years ago,'' Jackson wrote.
''It is always a great privilege to film here. You could search the world over and never find a more beautiful place ... Fran [Sir Peter's wife] and I are very proud to support the rebuilding of the Paradise Homestead and the efforts to protect this beloved part of Aotearoa.''
Paradise Trust chairman Tom Pryde said Sir Peter's endorsement was ''amazingly helpful'' at this difficult time.
On Saturday, the Glenorchy and wider communities were invited to an ''ashes picnic'' next to the remains ofthe homestead.
There, Mr Pryde announced Sir Peter's endorsement and words of support.
''It's fantastic that he has acknowledged what a special place it is and how special it is for his movies,'' Mr Pryde told the Otago Daily Times at the picnic.
He added that Jackson, a famously private person, was ''probably asked to support a thousand things a week''.
Now, the trust was looking ahead to the rebuild, and fundraising ventures were already under way.
Mr Pryde said the trust had decided against building a replica of the 131-year-old heritage building.
''It's [building a replica] not paying proper respect to what's been lost and it's just not the right thing to do ... as beautiful as the place was.''
The new building would retain the ideas of what Paradise embodied. It would be financially affordable, for all to enjoy a simple way of life, and would not become a luxury resort, like Blanket Bay or Matakauri Lodge.
A ''Friends of Paradise'' internet page has been set up. Discount books are being sold as a fundraiser.