Militants believed to be holding an Israeli soldier for more than a week have given Israel until 0300 GMT Tuesday to free Palestinian prisoners.
Israeli forces remain massed outside the Gaza Strip
A statement by Hamas' military wing and two other groups said Israel would otherwise have to face "the consequences", without giving details.
The Israeli government has said it will "not entertain blackmail".
Israeli soldiers entered southern Gaza last week and a small force of tanks was sent into the north on Monday.
Cpl Gilad Shalit was taken by gunmen in a cross-border raid on 25 June in which two other soldiers and two attackers were killed.
The Palestinian groups said Israel would "bear full responsibility for future consequences" if it did not meet the Tuesday deadline.
The faxed statement was signed by Hamas' Izzedine al-Qassam Brigades, the Popular Resistance Committees and the little-known Islamic Army.
There has been no independent confirmation of Cpl Shalit's condition since his capture, during which he was reportedly wounded.
The European Union has called for the immediate and unconditional release of the soldier, as well as the release of Hamas politicians detained by Israel last week in the West Bank.
Israelis will worry the ultimatum may mean their soldier will be killed, the BBC's Katya Adler reports from Gaza City.
SOLDIER CAPTURE TIMELINE
Sun 25 June: Cpl Gilad Shalit captured in cross-border attack
Mon 26 June: Palestinian Popular Resistance Committees demand prisoner releases in exchange for Shalit
Weds 28 June: Israeli military enters southern strip after launching air strikes on Gaza
Thurs 29 June: Israel detains dozens of Hamas officials
Sat 1 July: Groups believed to be holding Cpl Shalit demand 1,000 prisoners be released
Mon 3 July: Groups holding soldier issue ultimatum for 0300 4 July
Previously the militant groups involved in the corporal's capture demanded that all Palestinian women and young prisoners be released along with 1,000 male prisoners in exchange for information about the captured soldier's welfare.
Israel has ruled out any negotiations and is calling for the unconditional release of its soldier.
Foreign ministry spokesman Mark Regev told the BBC on Monday that the soldier should be released immediately and unconditionally.
"No-one in the Israeli government is going to entertain blackmail, no-one in the Israeli government is going to entertain the idea that these hostage- takers will dictate terms to the government," he added.
Israel has warned it will continue to target the Hamas-led government it holds responsible for the soldier's welfare and cross-border rocket attacks.
Israeli Prime Minister Ehud Olmert says Israel's army has been authorised to do whatever it takes to get its soldier back.
Israeli officials say Mr Olmert told his cabinet that he had given the army orders "to make sure no one sleeps at night in Gaza".
Hamas' military wing has said it will strike targets inside Israel if it does not leave Gaza again.
In the past, Hamas suicide bombers have struck many times in Israeli cities, the last time in Beersheba in August 2004, when 16 people died.
The entry of tanks and bulldozers into the north of the Gaza Strip is not part of a threatened large-scale incursion, Israeli sources say.
The aim, they say, is to search for tunnels and explosives used by militants, then return to Israel.
It is widely believed Israel's missing corporal is being held in southern Gaza while Israel's focus in the north is to crack down on Palestinian militants firing crudely made rockets at Israeli towns, our correspondent says.
It is, she adds, all part of keeping up the pressure on the Hamas-led government, blamed by Israel for the escalating crisis.
Over six nights of air raids Israel has mainly targeted empty buildings, fields and key infrastructure.
Gazans see this as collective punishment as essential supplies run low.
Five Palestinian militants have been killed since Israel began its offensive in Gaza, with the latest deaths occurring in clashes near Gaza's disused international airport where Israeli forces are concentrated.
In another development, Israeli troops raided a hospital in the West Bank town of Nablus in what is said to have been an unsuccessful bid to seize a wounded suspect.