Israel rejected international calls for a cease-fire today because Hamas fighters would "abuse" it to put themselves "in a better position for the next attack," Foreign Minister Tzipi Livni told ABC News.
In an interview with ABC News' chief Washington correspondent George Stephanopoulos, Livni said the cease-fire was unnecessary because Israel is keeping the border "crossings open during this operation" to allow "humanitarian aid to enter the Gaza Strip."
French Foreign Minister Bernard Kouchner had been pushing for a 48-hour cessation to hostilities to allow in food, medicine and supplies to help the 1.5 million Palestinians trapped in Gaza. Much of the international community, including the United States, has been urging Israel and Hamas to find a way to end the violence.
Although poor weather hampered visibility, Israel carried out missile strikes for the fifth consecutive day, targeting tunnels used to smuggle arms and supplies in through Egypt.
At the same time, Hamas fired more than 65 rockets and mortar shells into southern Israel, with five reaching as far as the city of Beersheva, 22 miles from Gaza. A Grad rocket fired from Gaza crashed through the ceiling of a Beersheva classroom this morning, which authorities had miraculously just called to evacuate.
"We need to change realities to stop the firing of rockets at Israel," Livni said in the face of the attacks. "At the end of the day, Hamas-controlled ... Gaza is a problem to Israel, a problem to the Palestinians and a problem to the entire region."
Livni would not rule out ordering Israeli armor and troops, which are massing outside Gaza, to launch a ground attack as well.
"I don't know yet. ... We are making our decisions on a daily basis," she told Stephanopoulos.
Livni indicated that the Gaza offensive is not about to be called off.
"We have a success, but of course it is not enough yet," she said.
The foreign minister, whose Kadima Party is running in national elections six months away, said a key aim of Israel is to "change the equation" with Hamas. Livni said Israel has succeeded at that.
"Hamas knows now that Israel is not willing to accept a situation in which its citizens come under attack. Israel is not going to show restraint when it comes to the safety of its citizens," she said.
Appearing from a bunker in Gaza, Hamas Prime Minister Ismail Hanieyh set his own conditions for a cease-fire.
"First, Israel must stop the aggression, lift the siege on Gaza and open the border crossings," he said.
Both sides want a cease-fire and to put an end to the violence, but only under their conditions. For both, a cease-fire wouldn't be a success unless they emerged from the fight appearing victorious to their people and to the international community.
President Bush spoke with Israeli Prime Minister Ehud Olmert by phone today to make a personal appeal for peace, but the two men did not discuss any timetable for Israel to cease its airstrikes into Gaza.
"President Bush thinks that Hamas needs to stop firing rockets, and that is what will be the first step in a cease-fire," White House spokesman Gordon Johndroe said.
Olmert assured Bush that Israel would target only Hamas, and that it's trying to avoid civilian casualties.
"We have to achieve a solution that will mean the civilian population of southern Israel no longer lives in constant fear of an incoming Hamas rocket," said Mark Regev, spokesman for Israeli Prime Minister Ehud Olmert.