(Clarifies anniversary in Dec. 2017 in bullet point)

* PM says land gift would cause constitutional problems

* Halti peak, on border, would be Finland's highest point

* Finland celebrates 100-year anniversary in December 2017

OSLO, Oct 14 (Reuters) - Norway's Prime Minister has dashed Finland's hopes of getting an Arctic mountain peak as a gift on its 100-year anniversary, saying there were constitutional problems in re-drawing the border between the two countries.

A campaign to give away the hard-to-wrap Halti mountain, which would make it Finland's highest point at about 1,330 metres (4,363 ft), would require moving the frontier by a few metres into Norway.

"Border adjustments between countries raise challenging legal problems, among them linked to the Norwegian constitution," Prime Minister Erna Solberg wrote on Friday to a mayor in northern Norway who has favoured the gift.

The 1814 constitution stipulates that Norway is "indivisible".

"We will instead consider another suitable gift to Finland on its anniversary," she wrote in the letter to Kaafjord Mayor Svein Leiros. Finland declared independence from Russia on Dec. 6, 1917.

"I'm disappointed, but I respect the fact that the decision is up to the prime minister," Leiros told Reuters. The campaign has won 17,000 likes on Facebook, with support from both sides of the border.

The founder of the campaign to give Halti to Finland, retired Norwegian mapping expert Bjoern Geirr Harsson, said he would not give up. "We will not take 'No' as an answer," he told Reuters.

Finland's highest point is now 1,324 metres, on a ridge of Halti. Moving the border fractionally into Norway would let Finland include a peak at 1,330 metres, he said.

New measurements showed the gift would involve handing over control of land a third the size of a soccer pitch and move the border by just 31 metres, he said.

He said that the constitution's insistence that Norway is indivisible reflected fears in the early 19th century that it could be torn up by big powers during the Napoleonic Wars, not lose a tiny patch of a barren Arctic mountainside. (Reporting By Alister Doyle, editing by Larry King)

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