JERUSALEM — The two most powerful players in the violent confrontation over the capture of an Israeli soldier by Palestinian Arab militants offered sharply differing visions yesterday on how to resolve the crisis.

The Hamas political leader, Khaled Mashaal, demanded a prisoner swap. Prime Minister Olmert said that would be a “major mistake.”

The men spoke within hours of each other — Mr. Olmert in Jerusalem, Mr. Mashaal in Damascus, Syria. Neither expressed any willingness to compromise, boding poorly for a quick end to Israel’s 12-day-old incursion into the Gaza Strip that has killed nearly 60 Palestinian Arabs.

“They will never be able to win from me any minor concession,” Mr. Mashaal insisted in his first public appearance since the June 25 capture of the 19-year-old Israeli soldier, Corporal Gilad Shalit.

Speaking to foreign reporters, Mr. Olmert saved some of his harshest rhetoric for the political head of Hamas, whose Islamic militants have staged dozens of suicide bombings in Israel.

“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.

At the same time, however, Mr. 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 because it hasn’t stopped Palestinian Arab attacks on Israel.

Corporal Shalit’s seizure in a cross-border raid and Israel’s harsh response have turned the already tense relations between Israel and the Palestinian Arabs’ Hamas-led government into a violent onslaught.

Four militants were killed in three Israeli airstrikes yesterday, and three others were killed in a fourth Israeli attack in northern Gaza last night. The army said the last attack targeted militants who had launched a rocket into Israel.

An 8-year-old girl was among five Palestinian Arabs wounded late Sunday by an Israeli missile attack targeting a car loaded with explosives. Rockets fired into Israel on Sunday wounded one person.

Dispelling press reports of a likely deal with Hamas, Mr. Olmert said, “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.”

But Mr. Mashaal insisted Israel must release some prisoners before Corporal 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 escalating their offensive will win the soldier’s release.

Mr. Olmert defended his army’s incursion, saying Israel had no choice but to launch it to win Corporal Shalit’s freedom and halt militant rocket fire into Israel. He rebuked European Union criticism that Israel is using disproportionate force, saying Palestinian Arab rockets terrorize tens of thousands of people 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.”

He declined to set any timetable for the incursion.

Mr. Olmert said Israel is not trying to topple the Palestinian Arab government, although he said Hamas leaders are “directly involved in terror.” His government has arrested dozens of Hamas political figures. “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.

Mr. Mashaal, who is considered more hard-line than Hamas leaders in the Palestinian Arab territories, said he held “Olmert and his hostile policies” responsible for what happens to Corporal Shalit.

He said he doesn’t fear Israeli threats to assassinate him because “I am yearning to meet God.”

Mr. Mashaal survived an Israeli assassination attempt in 1997.

“Today, Israel is really terrorizing our people,” he said. “Israel and America, which talked too much about this terrorism in the past, are the worst, severest, and ugliest examples of terrorism.”

Mr. Olmert ruled out negotiations with either Mr. Mashaal or the Hamas-led government that took power after winning legislative elections in January.

“This is not a government which is influenced by terror. This is not a government which sympathizes with terror. This government is terror,” Mr. Olmert said. He said the West Bank pullback would go forward.

“I am absolutely determined to carry out the separation from the Palestinians and establish secure borders,” he said.

Mr. Olmert wants to withdraw from most of the West Bank by 2010 to allow the Palestinian Arabs 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.”