"Our position is clear. We insist all aggressive military actions against the Palestinian people in the Gaza Strip stop, we demand all the troops be pulled back, the lifting of the siege and the opening of all crossings, with Rafah first," said Osama Hamdan, of Hamas Lebanon, in an interview with al-Jazeera television.
"This is the basic equation. This is our position and we hope the Egyptians will have a positive message, he added.
"Israel has found that it cannot eliminate the resistance," added Hamdan. "Israel cannot stop the rocket fire, even after 10 days of aerial assaults, navy fire and attacks on the ground – the rocket fire has not stopped. On the contrary, the resistance is now targeting strategic places in Israel."
Hamas military wing spokesman Abu Obaida reiterated the threats: "We tell the Israelis… Gilad Shalit misses you and we promised to get some soldiers to keep him company." Hamas, he added, will increase its use of long-range fire.
"We promise 11,000 prisoners that the Israeli incursion will be the dawn of a new day that will bring about their release, after we capture more Israeli soldiers.
"The enemy is flustered, the enemy has failed. It cannot hurt us, all it does is kill innocent women and children."
Obaida then warned Israel that "continuing the incursion will only make us increase our rocket range… but you are too foolish to understand. We will double the number of Israelis under fire. Our target bank is still wide."
Monday also saw Hamas senior official Mahmoud al-Zahar make his first televised appearance since the fighting in Gaza began, as he said that "the rockets our fighters are launching have broken Israel's grasp of security.
Hamas is going to great lengths to portray a resolute state of mind, rather than a defeatist one, yet despite the firm tone, Hamas heads still find it difficult to display a untied front; leading to many of their statements being taken for lip service to Syria and Iran, rather than an authentic stand.
Meanwhile, exiled Hamas leader Moussa Abu Marzouk said Monday that Hamas is open to international initiatives for a truce in Gaza but insists any proposal must guarantee Israeli withdrawal and an end to the blockade on the besieged territory.
Marzouk vowed that the Palestinian Islamic group would keep fighting an uneven war with Israel rather than return to the blockade: "Any initiative not based on ending the aggression, opening the border crossings and an Israeli withdrawal from the Gaza Strip has no chance of succeeding," he said.
"The defeat of the enemy and its failure to achieve its objectives must be reflected in the situation to come. I agree that the rules of the game must change, but in Hamas' favor," he added.
Abu Marzouk, deputy chief of Hamas' politburo, said that the group had decided to send a delegation to Cairo despite the group's misgivings about Egyptian help to Israel to enforce the blockade of Gaza.
"We know that Egypt is unhappy about Hamas' presence in Gaza. There isn't a complete proposal on the table. But let us wait... We are seeking an immediate ceasefire… The balance of power is uneven but we have the will and the capability to hurt the enemy," he said.
Ali Waked and Reuters contributed to this report