TOKYO, April 16 (Reuters) - Elliott Investment Management said on Thursday it has taken a stake in Daikin and thinks the manufacturer of air conditioners should improve margins and shareholder returns and review non-core assets.

Elliott did not provide further details on the stake.

A person familiar with the matter said Elliott's stake is around 3% and that it believes Daikin should do more to integrate its businesses, institute a share buyback programme and refocus on its core air conditioner operations.

Daikin has the capacity to allocate 1 trillion yen ($6.30 billion) to buybacks over the medium term, the person said.

Daikin said it was aware Elliott had taken a stake but declined to comment further.

Daikin's shares jumped 11% in morning Tokyo trading.

Elliott has been increasing its presence in Japan, scoring a landmark victory against automaker Toyota and taking stakes in companies including shipper Mitsui OSK.

($1 = 158.7700 yen)

(Reporting by Sam Nussey; Editing by Muralikumar Anantharaman and Himani Sarkar)

By Sam Nussey