The radical Al-Aqsa Martyrs Brigades announced the soldier would be killed unless Israel ended its military offensive in the Palestinian territories.
The armed group, loosely affiliated to Palestinian president Mahmud Abbas's Fatah party, called for "the end of the Israeli offensive" and "the lifting of the blockade" in the territories, in a statement received by AFP in Gaza City.
In his first public comments on the crisis since the campaign aimed at securing the release of the first captured Israeli soldier began, Mr Haniya said it was working towards freeing the 19-year-old corporal but that the "barbaric aggression" by Israel would not bring down the Hamas-led government.
"We are working to end this crisis but the aggression must stop and the siege has to be lifted," Mr Haniya said.
Later Israel launched air strikes for a fourth successive night against what it says are facilities used by terrorists.
Palestinians said the latest strikes hit uninhabited areas near the Khan Younis and Rafah refugee camps in the southern Gaza Strip.
In Gaza City a car reportedly carrying militants from Islamic Jihad was destroyed. Three people were wounded, Palestinian medical sources say.
Egypt, which is leading mediation in the crisis, said Hamas had agreed to secure the release of the soldier but that Israel had not agreed to the so far unspecified conditions.
Israel has already rejected a demand by militants to free Palestinian prisoners for information on Shalit's fate.
"Make no mistake, we are not going to negotiate on the release of our soldier," said cabinet minister Meir Sheetrit.
"If the kidnapped soldier Gilad Shalit does not return alive, there is no more Hamas government. Israel will erase this concept from the Middle Eastern political map," warned Israel's biggest selling daily Yediot Aharonot.
The head of Egyptian intelligence, Omar Suliman, is due to arrive in the region on Saturday for talks with both Palestinians and Israelis, while the United Nations Security Council is also due to debate the crisis this weekend.
"We are continuing our efforts and communications with the Egyptians, with the president (Abbas) and other parties to end this matter, but the Israeli escalation is putting up obstacles," Mr Haniya said.
Residency rights revoked
Israel revoked the East Jerusalem residency rights of a Hamas minister and three members of parliament, meaning their likely expulsion from the occupied east of the Holy City.
"The four are members of a terror organisation dedicated to the destruction of the state of Israel," an Israeli interior ministry official said.
Israeli troops had rounded up scores of Hamas members in a massive West Bank sweep the day before, including eight ministers - a third of the Palestinian cabinet - and 24 MPs.
In the first word on the kidnapped soldier's condition since Monday, Israeli public television reported that a Palestinian doctor had visited the captured conscript and treated his injuries at an undisclosed location in the Gaza Strip. The Israeli army refused to comment.
On Thursday night, fighter jets which blitzed Gaza with 30 air raids, striking the interior ministry, weapons depots and Hamas training camps, caused the first Palestinian casualty in the offensive.
A fighter from the hardline Palestinian Islamic Jihad movement was killed, while another militant from the Al-Aqsa Martyrs' Brigades, linked to Palestinian president Mahmud Abbas's Fatah party, was shot dead in the West Bank.
Israel has suspended plans to send ground troops into the north of the territory, amid international appeals for diplomatic efforts to free the kidnapped soldier.
"We are encouraged by the fact that the Israelis are standing down in Gaza and that Hamas is talking openly about repatriating the soldier," White House spokesman Tony Snow said.
In response to a call from the International Committee of the Red Cross for Israel to allow urgent medical supplies into Gaza, the Israeli army said it hoped to open the Karni Crossing next week to allow fuel and other supplies into Gaza.
Israeli defence Minister Amir Peretz has insisted that Israel, which has a force of about 5,000 troops massed on the border, has no intention of retaking Gaza, where about 1.4 million mostly impoverished Palestinians live.
But Israel has also issued warnings to Syria, accusing it of sheltering wanted Hamas militants, raising fears the conflict could spread.