As European diplomats poured into the region seeking a cease-fire, Israel and Hamas spoke defiantly of victory. Phones in Gaza homes rang repeatedly with recorded Israeli military messages saying, “We are getting rid of Hamas.” That goes beyond the stated goals of Israel’s top leaders, who have emphasized that the operation is intended to stop Hamas from firing rockets into Israel.

The Israeli foreign minister, Tzipi Livni, said after a meeting with officials from the Czech Republic, Sweden and France that Israel would “change the equation” in the region. She added that in other conflicts, “countries send in forces in order to battle terrorism, but we are not asking the world to take part in the battle and send their forces in  we are only asking them to allow us to carry it out until we reach a point in which we decide our goals have been reached for this point.”

The Hamas leader Mahmoud Zahar, speaking from a hiding place in a recorded speech on Hamas television, said: “The Israeli enemy in its aggression has written its next chapter in the world, which will have no place for them. They shelled everyone in Gaza. They shelled children and hospitals and mosques, and in doing so, they gave us legitimacy to strike them in the same way.”

Palestinian medical officials estimated that the death toll during the war reached 550 on Monday. The United Nations estimated that about a quarter of those killed were civilians.

Three Israeli soldiers were killed and 24 were wounded when an Israeli tank mistakenly fired at them Monday night, The Associated Press reported. Hamas has killed five Israelis since the conflict began.