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Israeli diplomats were open but skeptical regarding a cease-fire with Hamas, the terrorist organization one official labeled a “monster” with a “wish for death,” as U.S. Secretary of State John Kerry sought to bring an end to the fighting in Gaza.

“We didn’t want to be in this fight in the first place, but we’re not in the habit of committing suicide,” Paul Hirschson, spokesman for the Israel Foreign Ministry, told Fox News. “We’re up against what has turned into a monster which is essentially promoting the wish for death.”

Kerry landed in Tel Aviv even as a now-48-hour travel ban on U.S. air carriers was in effect, seeking to promote a potential cease-fire between the two sides in a war that has already cost more than 600 lives.

“Yes, it’s a good sign that Kerry is here, but we’re not going to sit around until such time [as it happens]” Hirschson said. “I wouldn’t rule it out, but it doesn’t look like Hamas is particularly interested.

Hisrchon noted that three cease-fire proposals have already been put forward: from the Egyptians, one from the UN and one from the International Committee of the Red Cross. But while Israel accepted each, Hamas rejected them.

Until both sides agree to lay down their arms, Hirschon said, Israel will continue its efforts to close off tunnels leading out of Gaza and kill operatives responsible for the daily barrage of rockets that fall into Israel.

“In parallel to these conversations” he said, “our military is moving forward in very difficult and complicated circumstances. We will cut off both arms of the Hamas military strategy; one, the rocket firing, and two, the tunnels. We are going to pursue both arms of the Hamas military network and chop them off piece by piece until there is a cease-fire.”

Hamas rockets have largely been neutralized by Israel’s Iron Dome protection system, but nonetheless exacted a price on Tuesday. A rocket fired from Gaza landed within a few miles of Ben-Gurion International Airport, prompting many international airlines to suspend flights to Tel Aviv. The ban was initially for 24 hours, but now some airlines -- and the FAA has already indicated it will be for longer -- could potentially prove the touch-paper that lights a further escalation in the latest conflict between Israel and the Gaza regime.

The extension of the flight ban could have a major impact -- both financial and psychological -- on Israelis, effectively cutting the country off from its main travel port, even though its sea lanes would remain open together with its smaller airports. Already thousands of visitors to Israel are struggling to get home, while others around the world are significantly delayed in returning to Israel.

A prolonged flight ban -- a prize beyond Hamas’ wildest dreams -- could prompt a harder crackdown by Israel on Gaza, to significantly increase the current bombardment from existing positions, or to advance further into the enclave. Israeli officials say they don’t want to pursue either option, but may have to if the rocket attacks effectively shut down the airport.

"Hamas rocket capabilities are very alarming; a rocket once a week at Ben-Gurion Airport is enough to wear Israel down and this is without taking into account the arms Hamas could obtain in the future,” said Avi Dichter, a former chief of Israeli security force Shin Bet.

Hirschon said Israeli efforts to minimize civilian casualties are dogged by Palestinian efforts to incur them – in what he believes is a bid for international sympathy.

“The Israeli military is taking unprecedented steps to try and avoid civilian casualties… but there is a very cynical abuse of the Palestinians by Hamas and the other groups,” said Hirschson. “It’s an endless abuse of their own almost as if they want casualties on the Palestinian side in order to wage a public relations war against Israel.”

Paul Alster is an Israel-based journalist who can be followed on Twitter @paul_alster and at www.paulalster.com