(Updates with Mitsui Fudosan's share reaction, Elliott's reaction)

Feb 5 (Reuters) - U.S. activist fund Elliott Management has called on Japan's biggest property group Mitsui Fudosan to launch a 1 trillion yen ($6.74 billion) buyback, the Financial Times reported on Monday.

Elliott's demands include the company sell down its $3.6 billion stake in Oriental Land, which runs Tokyo Disneyland, the report said, citing people close to the fund and Mitsui Fudosan.

Elliott's spokesperson declined to comment. Mitsui Fudosan officials did not have an immediate comment.

Mitsui Fudosan's shares were up more than 7% by early afternoon trade, having jumped nearly 12% earlier in the day.

Elliott's reported move comes as Japanese companies face increasing pressure to improve their market valuations and increase their returns on equity.

Nearly half of the companies on the Tokyo Stock Exchange's prime section have responded to a call to disclose plans to improve capital efficiency, the bourse said last month.

Optimism over improved investor returns had also helped propel the Tokyo market to its highest level in more than three decades last year.

($1 = 148.4600 yen) (Reporting by Disha Mishra in Bengaluru and Mariko Katsumura in Tokyo; Editing by Savio D'Souza and Jamie Freed)