(Adds Carter statement, details, background)

JERUSALEM, June 9 (Reuters) - The family of Gilad Shalit, an Israeli soldier abducted by militants in the Hamas-controlled Gaza Strip, received a hand-written letter from him, Israeli officials said on Monday.

Shalit, then 19, was captured on June 25, 2006 by Palestinian gunmen who tunnelled into Israel from Gaza. There has been no sign of life from the captive soldier except for a letter in September 2006 and an audio tape released by Hamas last June.

Shalit's family was not available for comment.

The release of the letter comes as Egypt is trying to broker a truce between Israel and Palestinian militant groups in Gaza.

A senior Hamas official said the letter was released in a gesture to former U.S. President Jimmy Carter who met with the group's leaders during a trip to the region in April.

"The letter was sent in a goodwill gesture to former President Jimmy Carter and to indicate Hamas's seriousness in its desire to reach a prisoner swap deal that will close the Shalit file and fulfill the demands of the Palestinian groups who abducted Shalit," Osama al-Muzaini told Reuters.

The Carter Centre said in a statement it had received the letter at their office in Ramallah on Sunday and passed it on to Shalit's parents.

Hamas, one of three militant groups that claimed responsibility for the joint operation in which Shalit was abducted, has said it will not release him unless Israel meets its demand to free nearly 1,400 Palestinian prisoners, including 350 with life sentences. Israel has rejected these terms.

Hamas Islamists took control of the Gaza Strip after routing forces loyal to Palestinian President Mahmoud Abbas. (Writing by Ari Rabinovitch; Editing by Diana Abdallah)

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