Militant groups in Gaza have demanded the release of Palestinian children and women from Israeli jails before giving information about a missing soldier.
Israeli armour has been assembling on the Gaza border
It is the first such statement since the suspected abduction of Israeli tank gunner Gilad Shalit during clashes on the Gaza border on Sunday morning.
The signatories included the armed wing of the governing party Hamas.
Israeli Prime Minister Ehud Olmert said there would be no releases and warned of military action to free the soldier.
"The question of freeing [Palestinian] prisoners is in no way on the Israeli government agenda," Mr Olmert said during a speech in Jerusalem.
"There will be no negotiations, no bargaining, no agreements."
Cpl Shalit was believed to have been taken captive by militants who tunnelled out of Gaza to attack the army post at Kerem Shalom.
Two Israeli troops and two militants were killed during the raid.
Mr Olmert has put the army on standby for an extensive military operation against Palestinian militants and Israeli tanks and armoured vehicles have assembled on the Gaza border.
Hamas political leaders have denied any knowledge of the soldier's whereabouts - but they have called for him to be well treated.
The faxed statement was signed by the Popular Resistance Committees umbrella group, Hamas's Izzedine al-Qassam Brigades, and the previously unknown Army of Islam.
It said: "The Occupation [Israel] will not get any information about its missing soldier until it commits to the following:
"First, the immediate release of all women in prison. Second, the immediate release of all children in prison younger than 18."
Israel is believed to have incarcerated about 100 women and 300 under-18s among the 9,000 Palestinian prisoners it is holding in its jails.
Intense diplomatic efforts have been under way since the soldier's disappearance, including mediation by an Egyptian delegation in the Gaza Strip.
This was noted by the kidnappers themselves, who said their demands were "in response to various mediation efforts and other intervention".
The statement did not confirm whether the three groups were holding Cpl Shalit captive themselves.
Israeli officials have held Palestinian Authority President Mahmoud Abbas and Prime Minister Ismail Haniya, of Hamas, responsible for the 19-year-old Israeli's safety.
Correspondents say the crisis could spoil efforts to bind Hamas into a plan implicitly recognising Israel, and may expose divisions between hardline and more pragmatic Hamas elements.