"We don't want a ... quick fix and in two weeks or two months we have another round," he said. "'The people of southern Israel have the right to live normal lives, not in fear of incoming missiles."
Israeli military spokeswoman Lt. Col. Avital Leibovich said Israel's offensive is meant to "cripple the capabilities" of Hamas and other militant groups in Gaza. Leibovich said Israel's air force has specified hundreds more targets for attack, adding that "we are really determined to reach the goal of the operation."
However, Israeli leaders face diplomatic restraints as they consider the next military move, including a possible ground invasion. President Barack Obama and British Foreign Secretary William Hague on Sunday cautioned against an escalation in Gaza, including sending in ground troops, even as they asserted that Israel has the right to defend itself against rocket fire.
A Gaza invasion or dramatic escalation of the air campaign could further strain Israel's ties with Egypt, a regional powerhouse and Israel's main conduit to the Arab world. Israeli Vice Premier Moshe Yaalon said Sunday that Israel is keeping open channels with the Egypt, adding that "we hope the Egyptian regime will play a positive role."
The Egyptian-led cease-fire efforts are taking place against a regional backdrop that is dramatically different from what it was four years ago, during Israel's last major Gaza offensive.
At the time, Hamas was largely isolated. Now, following the Arab Spring uprisings, it has new regional friends, including fellow Muslim Brothers in power in Egypt and Tunisia, and increased support from Qatar and Turkey. On Sunday, Hamas' Mashaal also met with Turkish Prime Minister Recep Tayyip Erdogan, who is visiting Cairo.
Both Yaalon and Ahmed Yousef, a Gaza intellectual close to Hamas, suggested that the two sides will keep fighting to improve their positions in eventual truce talks.
Israel is trying to improve its leverage by striking Hamas hard, said Yaalon. "We have to deter them," he said. "How? By charging them the heavy price right now where they'll have to consider whether they'll go on with their terrorist attacks ..."
Yousef said Hamas is capable of firing rockets as long as Israel bombards Gaza, adding that militants "have enough missiles to fire." Overall, Hamas is in a strong position to negotiate a truce deal, he said, citing the new diplomatic support and the group's current popularity at home, in addition to the large arsenal.
The current round of fighting will eventually grind to a halt, but it's unlikely the two sides will emerge with a durable cease-fire, said Israeli analyst Yossi Alpher.
"Both sides will have to come down from their lofty demands, and it will require some heavy pressure," he said. "Certainly, it will end with some sort of cease-fire, but it won't be kept because Hamas will be rearming and Israel will respond and things will get out of hand within a few months."
Bohn reported from Jerusalem. AP reported Ibrahim Barzak in Gaza City contributed to this report.