"The question is not whether we want it or not, but whether or not it is possible," she told demonstrators after she invited them into her home.

And she added: "It is important for me to stress to every soldier and everyone who is enlisting in the army that we are still in a fight for Israel's existence, that the government is responsible for every IDF soldier and that every one of us wants every soldier to return home."

Shalit, 22, was captured in a cross-border raid near the Gaza Strip by Palestinian kidnappers on June 25, 2006, and has been held hostage by Hamas ever since.

He was a corporal at the time he was snatched but has since been promoted to staff sergeant.

Livni, who is also leader of the Kadima party, told the protesters: "Today there is a sense that Gilad Shalit's release is a question of whether the government wants to bring him back or not.

"If someone who enlists in the army is asking himself whether the government would want to release him or not, that is terrible in my eyes."

On the day she met the protesters, 150 demonstrators also gathered outside Prime Minister Ehud Olmert's Jerusalem home, calling on him to secure Shalit's release before the end of his time in office.

Earlier, Livni had hinted at a Tel Aviv high school that Shalit might remain in the hands of Hamas in Gaza for some time to come.

One of the demonstrators, Guy Elyasaf, expressed disappointment with the foreign minister.

"It has given us a feeling that Israel does not take responsibility for a soldier that falls into captivity," he said.

Pushed to explain her stance, Livni told Israel radio: "I will never negotiate his release in the media.

"I consistently refused and continue to refuse to politicise the issue by saying that some want him back more than others.

"We all want him back, [but] we cannot bring every soldier home."

However, Defence Minister Ehud Barak later disagreed with her when he said in Holon: "In order to return Gilad we'll have to make tough decisions, some of which also hold risks, but I'm willing to take the responsibility in order to see him among us.

"The last think we should do is renounce responsibility."

And IDF Chief of General Staff Gabi Ashkenazi said: "There is not a day where the subject of Gilad Shalit goes off the agenda."