But on Monday, the Supreme Court rejected the appeal, saying that while it understood the plight of Shalit's family, any court intervention in political matters must be very limited.
Shalit was captured on June 25, 2006, by Palestinian fighters who tunnelled into Israel from the Gaza Strip.
His case is expected to be part of the discussions Ehud Olmert, Israel's prime minister, is scheduled to hold on Tuesday in Egypt with Hosni Mubarak, Egypt's president.
Egypt brokered the truce that went into effect on Thursday between Israel and the Gaza Strip's Hamas rulers.
Shalit's family had asked the court to prevent the implementation of any agreement to ease Israel's blockade of the Gaza Strip until the soldier was freed or a guarantee for his release was given.
|Gilad Shalit was captured during a Hamas raid two years ago [EPA]
Israel cut back the supplies of fuel and other goods into the Gaza Strip after Hamas seized the territory from the Fatah movement of Mahmoud Abbas, the Palestinian president, a year ago.
As part of the ceasefire, operations have been stepped up at the Israeli-run Karni and Sufa crossing, with the flow of goods set at 30 per cent of the levels before Hamas took over Gaza.
But Gaza's crossing with Egypt, at Rafah, remains closed and its renewed operation is widely seen as linked to efforts to secure a prisoner exchange deal between Israel and Hamas.
Meanwhile, the Israeli military said it had begun a procedure that could lead to a declaration that two soldiers captured by Lebanese Hezbollah guerrillas two years ago are dead.
The military statement said all the information about the soldiers has been transferred to the chief military rabbi, Brigadier-General Avichai Ronsky, who will determine whether they will be declared as killed in action.
The soldiers were known to be badly wounded when they were captured.
The move on Monday comes as Israel and Hezbollah were said to be close to a deal to trade the soldiers for Samir Kantar, a Lebanese serving multiple life terms for a 1979 attack that left four people dead.