The Palestinian group Hamas has confirmed for the first time that a captured Israeli soldier is alive.
Cpl Gilad Shalit was captured on 25 June
It said Cpl Gilad Shalit was being treated well and humanely.
Israel launched an incursion into Gaza to find Cpl Shalit after his capture on 25 June. Some 30 Palestinians have been killed in the past few days.
Palestinian President Mahmoud Abbas urged an end to Israel's "aggression" while UN head Kofi Annan said both sides must "pull back from the brink".
The Hamas statement appeared to soften the group's demands for the release of Cpl Shalit, who was captured in a raid on a border post.
It said that Hamas was only calling for Israel to free Palestinian women and children held in its jails.
There was no mention of a previous demand that an additional 1,000 prisoners also be freed, including prominent militant leaders.
Hamas said the ball was in Israel's court and was critical of Israel's leaders for so far refusing to negotiate.
Israel on Friday sent conflicting signals about possible prisoner releases.
A spokesman quoted Interior Minister Avi Dichter as saying that Israel "knows how to carry out a release of prisoners as a goodwill gesture".
But Interior Minister Roni Bar-On later said on television: "I have just spoken to Prime Minister Ehud Olmert and our position remains unchanged: we refuse to negotiate with Hamas and [Palestinian] prisoners will not be released."
Israel has said it will do everything possible to free Cpl Shalit.
The BBC's Alan Johnston in Gaza says Hamas' statement was different from previous pronouncements, which had come from the military wing.
He says there has been speculation about possible splits within the movement and some observers will have reservations about the significance of this statement until they hear the influential military men have endorsed it.
On Friday, Mr Abbas called both for Palestinian militants to release Cpl Shalit and for Israel to free Palestinian prisoners.
About 30 Palestinians have died in the past few days
"The world must stop this aggression and this inhumane invasion so that our [mediation] efforts can get somewhere," he said.
The European Union accused Israel of using "disproportionate" force and making a humanitarian crisis worse during operations in Gaza.
The EU is Israel's largest trading partner and rarely criticises the country in such terms on military or security matters.
UN Secretary General Kofi Annan appealed to both sides "to pull back from the brink for the sake of all civilians in the region".
He called on the UN Security Council to take a stand on the issue.
The council has debated a draft resolution demanding an immediate Israeli withdrawal from Gaza and the release of detained Palestinian officials.
The draft was presented by Qatar on behalf of the UN's Arab Group, but appears doomed in view of opposition from the US, which has the power of veto.
The US ambassador to the UN, John Bolton, said the document was "not balanced".
Israel's incursion into Gaza is its biggest military operation there since it ended its 38-year occupation nine months ago.
Five people were killed on Friday, taking the total number of Palestinians who have died in the past few days to about 30.
Most of the dead were militants, but a number of civilians have also been killed. One Israeli soldier has been shot dead.