For six days, Israel has carried out a large-scale air offensive in Gaza, aiming to halt destructive and sometimes deadly rocket launches emanating from the Palestinian territory.

Monday saw more carnage, more heated words and more damage on both sides. There was also more movement toward a possible intensification as Michael Oren, Israel's ambassador to the United States, said Israel had finished its planning for a ground invasion of Gaza.

If Israeli troops do invade, Hamas leader Khaled Meshaal said it would "not be a picnic."

"We do not want escalation, nor do we call for a ground war," he said Monday. "But we are not afraid of it, nor will we back down."

All this violence and rhetoric has intensified international efforts to find a diplomatic solution to the crisis, starting with a cease-fire.

"This must stop," U.N. Secretary-General Ban Ki-moon said late Sunday.

A steady stream of U.N. and European diplomats have and will be traversing the region trying to calm the situation.

On Monday, Ban and an Israeli delegation went to Egypt, where that nation's top intelligence official presented Israel a letter outlining Hamas' proposal for a cease-fire, said a general in Egyptian intelligence who is optimistic about a deal being reached. The fighting has challenged Israel's relationship with Egypt, yet Israeli President Shimon Peres on Monday praised Egyptian President Mohamed Morsy for playing a "constructive role."

Israeli foreign ministry spokesman Yigal Palmor confirmed late Monday that "negotiations are going on" that may lead to a cease-fire, though he didn't offer any details.

Meanwhile, Arab League Secretary-General Nabil el-Araby and 16 foreign ministers from the league's member states were to arrive in Gaza on Tuesday, to be joined by Turkish Foreign Minister Ahmet Davutoglu, a spokesman for the organization said.

Gaza itself has been under a crippling economic embargo since Hamas won control of the territory from the Fatah-led Palestinian Authority, which controls the West Bank, after a landslide 2007 election that was followed by intra-Palestinian clashes. The United States, Israel and the European Union characterize the militant fundamentalist Islamic organization Hamas as a terrorist group.

In the West Bank, Palestinian Authority President Mahmoud Abbas will hold talks with the U.N. secretary-general, according to Saeb Erakat, a member of the PLO's executive committee and an Abbas ally. The West Bank has been relatively quiet, though a Palestinian protester did die Monday -- two days after he and others clashed with Israeli troops -- Ramallah Medical hospital director Ahmad Bitawi said. And Israeli troops shot and killed a 22-year-old Palestinian near Hebron, witnesses said.

Diplomats hope to avoid a repeat of 2008, when at least 1,400 died as Israeli troops invaded Gaza after a similar spate of rocket attacks.

Israel has signaled it is open to a cease-fire, but only if Gaza militants halt rocket attacks. Air raid sirens yet again resounded all day Monday around Israel, where rocket attacks have killed three and wounded 68 according to Israeli officials.

The bloodshed might be worse if not for the "Iron Dome," Israel's missile defense system that has intercepted about 30% of the rockets fired from Gaza since last week, including more than half the 67 fired on Monday, according to the Israel Defense Forces. The missile defense system intercepted several more rockets fired Monday at Ashkelon, the IDF said. But several rockets hit Eshkol, also in southern Israel, with one striking a closed school.

"They have a choice. The minute they will stop (shooting), it will stop," Peres said.

Israeli government spokesman Mark Regev said a short-term "Band-Aid" solution won't do.

"There's no doubt that Hamas would agree to an immediate cease-fire, but it wouldn't mean anything. We want to know when it's over, that it's really over," he said, adding Israel will use diplomacy or military force -- whatever is necessary -- to ensure that southern Israel doesn't continue to face the threat of rockets.

Like Regev, Qatari Prime Minister Sheikh Hamad Bin Jassim al Thani said there can't be a repeat of 2008 -- though he has a different view as to why.

Having gone to Gaza a few weeks ago and observed "the miserable life" of residents there, Sheikh al Thani told CNN's Christiane Amanpour it's not tenable for there to be more assassinations of Hamas leaders and Israeli forces surrounding Gaza, as was the case four years ago.

"(Hamas wants) a complete package for the cease-fire," he said.

Palestinian health officials said 104 people, among them women and children, have been killed -- at least 24 on Monday. They also say 860 have been wounded in Gaza since Israel began its offensive in response to what Israel characterized as incessant rocket attacks by militants.

Israeli authorities say they take great pains to avoid civilian casualties, though this is difficult to do when rockets are being launched from densely populated civilian areas, where suspected militant leaders are also based.

While saying he feels an agreement can be reached, Palestinian parliament member Mustafa Barghouti says he blames Israel for the bloodshed thus far.

"The problem is that Israel is using the bombardment of civilians and the killing of children as a tool of negotiations," he said.