The militants have demanded that women and minors held in Israeli prisons go free, in exchange for information on the soldier, "The Occupation (Israel) will not get any information about its missing soldier unless it abides by the following: release all female prisoners in Israeli jails ... and children under the age of 18," a written statement said.
Issued by Hamas’s military wing, Izz el- Denn al- Qassam Brigades, the Popular Resistance Committees and the Islamic Army, "Military Statement 1" did not confirm that the groups were holding Corporal Gilad Shalit nor give details of his condition.
Demands rejected
Their demand to release prisoners was rejected by Israeli Prime Minister Ehud Olmert, "The question of releasing prisoners is not on the agenda of the Israeli government at all," he said in a speech in Jerusalem after the statement was released.
"The time is approaching for a comprehensive, sharp and severe Israeli operation. We will not wait forever… We will not become a target of Hamas-terrorist blackmail." Mr Olmert added.
Sunday's raid which saw the militants dig under a border fence, killed two soldiers, two militants and the disappearance of Mr Shalit. It was the first such incident since Israel quit the Gaza Strip last year.
Earlier, an anonymous telephone conversation with a representative of the Popular Resistance Committees told news agency AFP that it was holding the soldier, "He is alive and in good health… He is not seriously injured."
But the representative gave no indication as to the whereabouts of Mr Shalit, whose bloodstained flak jacket was found near the scene of the attack.
Mr Olmert said that he held both the governing Hamas movement and President Mahmoud Abbas responsible for the assault, appearing to dash any chance of talks with the moderate leader in the near future.
Reprisals
Israel has vowed reprisals for the abduction, which could include a re-invasion of Gaza, the coastal territory it quit last year after 38 years of occupation, or the assassination of leaders of Hamas, an Islamic militant group dedicated to its destruction and the democratically elected government.
Unless the soldier if freed, a high- ranking security official has also threatened that Israel would work to topple the Hamas-led government, which is already boycotted financially and politically by most of the international community.
"We will make sure that the Hamas government ceases to operate if the kidnapped soldier is not returned to us alive," the unnamed source told AFP.
Under intense pressure to resolve the crisis, Mr Abbas ordered his security services to launch a massive manhunt for the kidnapped conscript - a step which is hoped will avert a possible wide-scale Israeli assault.
Calls for restraint
The international community has called for the soldier’s immediate release, but the United States, the European Union and the United Nations’s Secretary General Kofi Annan have also all called on Israel to show some restraint.
"We urge both sides to exercise restraint and avoid steps which further escalate the situation," US State Department spokesman Sean McCormack told reporters.
Mr Annan urged, through a spokesman, for all parties involved to "exercise restraint at this grave moment, and to take all possible steps to avoid further escalation and bloodshed."
Israel’s Housing Minister Meir Sheetrit told AFP that the government would first give diplomacy a chance, "We decided not to have an immediate military reaction and give diplomacy a chance," he said. "We will not let anger dictate our reaction."