SYDNEY (Reuters) - Australia's Prime Minister Malcolm Turnbull on Tuesday settled the nation's longest-running land rights claim, handing Aborigines land title deeds wrapped in eucalyptus paperbark to a peninsula on Darwin harbor in the tropical north.

The Kenbi land claim, covering 676 square kms (261 square miles) of the Cox Peninsula west of Darwin, was first lodged by a group of Larrakia Aboriginal people 37 years ago in 1979.

"We formally recognize what Larrakia people have always known: That this is Aboriginal land," Turnbull said in a televised speech on the Cox Peninsula.

"I acknowledge that the Larrakia cared for this country for tens of thousands of years and that your songs have been sung since time out of mind," he said.

Australia's aboriginal people were dispossessed when the continent was colonized by Britain in the eighteenth century, but native title laws now allow land claims if Aborigines can prove an unbroken association with the land.

"I am very happy after 37 years, we have got our land back," aboriginal landowner Jason Singh told the Australian Broadcasting Corporation. "I am very sad that our mums are not here today."

Aboriginal native title now covers more than 2.4 million square kms (926,000 square miles) of Australia, or 31 percent of the national landmass.

Australia's roughly 700,000 indigenous citizens, who track near the bottom of its 23 million citizens in almost every economic and social indicator, see native title as recognition of their place as Australia's first people.

(Reporting by Tom Westbrook; Editing by Michael Perry)