In his first interview, Sgt Shalit told Egyptian TV he missed his friends and family.
BBC: Gilad Shalit freed in Israeli-Palestinian prisoner swap
We are pleased by the reports that Mr. Shalit will be home soon with his family.
They also reportedly claimed that the interview violated the terms for Sgt Shalit's release.
Noam and Aviva Shalit are urging the outgoing PM to agree a prisoner swap.
Noam Shalit said his son pleads for his release and asked to be rescued in the letter.
Sgt Shalit was snatched in a cross-border raid by Hamas militants who tunnelled from Gaza into Israel.
But Israel stopped the EU operation after Hamas seized an Israeli soldier, Gilad Shalit, in June 2006.
Mr Shalit turned out to be alive, and his captors promised the Turks they would treat him respectfully.
ECONOMIST: Sometimes Turkey really is a bridge between west and east
Afterwards, Sgt Shalit was handed to Israeli authorities, given a medical check and allowed to call his family.
Carter also asked Hamas to release Shalit, Meshaal said after the former president's visit, but the request was rejected.
Sgt Shalit is to be transferred from Hamas custody to Egypt, who would then hand him over to Israel.
Sgt Shalit was freed on Tuesday as part of an elaborate prisoner exchange.
His father, Noam, confirmed to CNN that the letter was in Shalit's handwriting and appeared to have been written recently.
The Egyptian journalist who interviewed Israeli soldier Gilad Shalit just after Hamas freed him has defended herself against Israeli criticism.
Olmert has been under pressure to secure Shalit's release as part of a broader cease-fire deal with Gaza's Hamas leadership.
CNN: Olmert blasts 'damaging' reports on kidnapped Israeli soldier
Despite all this, I am pleased that Gilad Shalit has been reunited with his family, as have many Palestinians, including Omar.
Sgt Shalit was later taken to Tel Nof airbase, where he met his family, and was passed fit by Israeli army doctors.
BBC: Gilad Shalit freed in Israeli-Palestinian prisoner swap
Shahira Amin said she had not forced the interview on Sgt Shalit, and that it was important to let people see him.
We are pleased that Gilad Shalit has been reunited with his family.
France's president, Nicolas Sarkozy, summoned Corporal Shalit's father to Paris to reassure him that his son, a dual French-Israeli citizen, was still alive.
It is clear that we all hope that the day when Gilad Shalit returns to his family will come as soon as possible.
CNN: Olmert blasts 'damaging' reports on kidnapped Israeli soldier
Israel's government also hopes to wrest the return of a kidnapped soldier, Gilad Shalit, as part of a post-war package of understandings negotiated through Egypt.
ECONOMIST: Israelis begin to ask whether the war in Gaza was worth it
During the interview Ms Amin asked Sgt Shalit if he would campaign for the release of more than 5, 000 Palestinian prisoners still in Israeli jails.
Shalit was 19 when he was captured on June 25, 2006, by Palestinian militants in Gaza, including those from Hamas, which now controls the territory.
CNN: Olmert blasts 'damaging' reports on kidnapped Israeli soldier
Olmert and Peretz hope to somehow convince Hamas and Fatah and their bosses in Damascus and Teheran that they are better off coughing up Shalit.
CENTERFORSECURITYPOLICY: Olmert's response to Palestinian violence
Gilad Shalit was feared to be gravely ill, perhaps even dead.
ECONOMIST: Sometimes Turkey really is a bridge between west and east
The only exception is, of course, the issue of the Israeli serviceman Gilad Shalit, who has been held hostage now by Hamas for all too long.
During his press conference with Blair, Olmert renounced his previous well-considered demand that Shalit be released before any meeting can take place between him and Abbas.
Reports have again begun to circulate that Hamas may free an Israeli corporal, Gilad Shalit, who has been held by Hamas in Gaza for three years.
ECONOMIST: The Palestinians look both divided and leaderless
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