Hamas political leader Khaled Mashaal demanded a prisoner swap, while Israeli Prime Minister Ehud Olmert said that would be a "major mistake."
The two men spoke within hours of each other — Olmert in Jerusalem, Mashaal in Damascus, Syria. Neither expressed any willingness to compromise, boding poorly for an end any time soon to Israel's 12-day-old Gaza Strip incursion that has already killed 58 Palestinians.
"They will never be able to win from me any minor concession," Mashaal insisted in his first public appearance since the June 25 capture of the 19-year-old Israeli soldier, Cpl. Gilad Shalit.
More violence in Gaza signaled that neither side is willing to back down. Gaza's main hospital was in a frenzy over injuries, and at least four people were killed and two critically injured, CBS News chief foreign correspondent Lara Logan reports.
Speaking to foreign reporters, Olmert saved some of his harshest rhetoric for Mashaal.
"Khaled Mashaal is a terrorist with blood on his hands. He's not a legitimate partner for anything. He's not a partner and he won't be a partner. I will not negotiate with Hamas," the Israeli leader said.
Speaking to foreign reporters, including CBS News correspondent Robert Berger, Olmert said any other country that had a thousand rockets fired at its sovereign territory would do the same thing. But Olmert said the violence in Gaza would not deter him from carrying out his plan to leave the West Bank, despite a growing sentiment among Israelis that last year's Gaza pullout was a failure.
In other developments:
In addition to the four militants killed in three Israeli airstrikes Monday, three others were killed in a fourth Israeli attack in northern Gaza on Monday night. The army said the last attack targeted a group of militants who had just launched a rocket into Israel.
One doctor told Logan it was the worst situation he had seen in his 40 years.
"We see death everywhere we go," said Shifa Hospital emergency room manager Dr. Jumaa al-Saqa.
Dispelling media reports of a likely deal with Hamas, Olmert said that "trading prisoners with a terrorist, bloody organization such as Hamas is a major mistake that will cause a lot of damage to the future of state of Israel."
Wearing the Palestinian checkered scarf draped over his shoulders, Mashaal insisted Israel must free at least some prisoners before Shalit can be freed.
"The solution is simple: an exchange. But Israel refuses that," he said, adding that the Israelis are "under an illusion" if they think that by escalating their offensive they will win the soldier's release.
Olmert defended his army's incursion, saying Israel had "no choice" but to launch it in order to win Shalit's freedom and halt a barrage of militant fire into Israel. He rebuked European Union accusations that Israel was using disproportionate force, saying Palestinian rockets were terrorizing tens of thousands of residents in southern Israel.
"When was the last time that the European Union condemned this shooting (of rockets) and suggested effective measures to stop it?" he asked. "I can imagine that some of those countries that preach to us would have done a lot more, in a more brutal and vicious and cruel way against civilian populations, than what we did ... in order to defend our people."
Israel expanded the operation last week into northern Gaza to halt months of rocket attacks. Tanks and ground forces have entered the area, and Israel has carried out numerous airstrikes, leading to widespread destruction.
Olmert said Israel is not trying to topple the Palestinian government, though he said Hamas leaders are "directly involved in terror." His government arrested dozens of Hamas political figures after Shalit's seizure.
"We have no particular desire to topple the Hamas government as a policy. We have a desire to stop terrorists from inflicting terror on the Israeli people," he said, declining to give a timetable for the operation.
Mashaal, who is considered more hard-line than local Hamas leaders, said he held "Olmert and his hostile policies" responsible for what happens to Shalit.
He said he doesn't fear Israeli threats to assassinate him because "I am yearning to meet God."
Mashaal survived an assassination attempt in 1997 during which Israeli agents in Jordan squirted poison into his ear before Jordan's King Hussein compelled Israel to deliver an antidote.
"Today, Israel is really terrorizing our people," Mashaal said. "Israel and America, which talked too much about this terrorism in the past are the worst, severest and ugliest examples of terrorism."
Olmert spoke similar words when he ruled out negotiations with either Mashaal or the Hamas-led government.
"This is not a government which is influenced by terror. This is not a government which sympathizes with terror. This government is terror," he said.
Olmert said that the West Bank pullback would go forward despite indications that Israelis' support for such a withdrawal has been hurt by the violence that followed the Gaza pullout, including the current standoff over Shalit.
"I am absolutely determined to carry out the separation from the Palestinians and establish secure borders," he said. Olmert wants to withdraw from most of the West Bank by 2010 to allow the Palestinians to gain independence and to secure a long-term Jewish majority for Israel
"We want to separate in a friendly manner and to live alongside each other ... in a peaceful way," he said. "If the terrorist organizations will impose a violent confrontation, both Israelis and Palestinians will have to bear the consequences. That can't stop the inevitable process of separation of Israelis and Palestinians."