The parties had been in negotiations for more than 12 months since Telstra received $10.7 million to build three towers on Flinders Island and another on Cape Barren Island.

The Flinders towers have been completed, but a dispute over land values on Cape Barren held up the construction to a point where it could not be finished by the end of 2019 - a condition of the Building Better Regions Fund.

Telstra carried out an independent valuation of the agreed Cape Barren site, at Porky Boat Harbour, offering the ALCT $6000 for the purchase along with a digital inclusion program for the island's 100 residents.

The ALCT saw this offer as insufficient and questioned Telstra's valuation.

ALCT chairperson Michael Mansell said Teltra's offer was "measly" and it was one of the first times they had failed to reach a lease agreement for Aboriginal-owned land in Tasmania.

"We've never had this problem before. When private interests want to lease any Aboriginal land, we sit down with them and negotiate terms for them, and always come to an agreement," he said.

"When government departments want to lease land, we've never had a problem.

"We lease out about 15 areas of Aboriginal-owned land, and we never had an issues with lease holders except for Telstra."

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The Porky Boat Harbour site was the third that Telstra had considered, after it was knocked back from building at an existing exchange, and at a site owned by Flinders Island Council.

With negotiations abandoned, Cape Barren will continue to rely on patchy overspill coverage from the south of Flinders Island.

Telstra's Tasmanian regional general manager Michael Patterson said the ALCT had "shown no willingness to compromise" and their offer was 50 per cent above their valuation.

"The latest offer was extremely generous and included additional social, community and technological support for locals on Cape Barren Island - but the ALCT rejected this too and let their own community down," he said.

"Telstra determines reasonable rents in line with independently assessed site values and whether the economics stack up."

Mr Mansell claimed Telstra had taken a different approach to Cape Barren because it was Aboriginal-owned land, but Mr Patterson rejected this assertion and said "race plays no part in the assessment of our sites".

The tower would have acted as a 3G and 4GX base station for Cape Barren.