Updated

Israel's political and military leaders authorized the army on Monday to intensify ground operations against Palestinians in Gaza who have been pounding Israeli border towns with deadly rocket fire. Military officials said, however, that a major thrust into the densely-populated coastal strip is not in the works.

Frequent air sorties over the past two weeks have made leaders of the radical Islamic Hamas movement lie low, with Prime Minister Ismail Haniyeh missing a Monday Cabinet meeting in Gaza City.

Hamas says it is responsible for the recent wave of rocket attacks, in which two Israeli civilians died and thousands fled the border region.

Palestinian President Mahmoud Abbas appealed to militant groups Monday to take the first step in forging a fresh truce with Israel, saying the alternative would be the collapse of the Palestinian coalition government.

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The militants have said there could be no truce if Israel keeps up its attacks and refuses to extend any Gaza cease-fire to the West Bank, site of frequent Israeli swoops on militants but in an interview with Associated Press Television News, Abbas said it was the Palestinians who should take the first step.

"The truce project means all acts by all parties stop, the Palestinians first and the Israelis, so we can move after to the West Bank," Abbas said. "Israel...can do what it wants, whenever it wants but we say we should do our duties and put the ball in the Israeli court."

Under the new Israeli directive, larger numbers of troops will be able to enter Gaza on pinpoint missions, but no widespread campaign is imminent, the military officials said, speaking on condition of anonymity because they were not authorized to discuss policy.

Past large-scale offensives have failed to quell the rocket fire.

The green light to send more troops into Gaza was given on Monday by Prime Minister Ehud Olmert, Defense Minister Amir Peretz and military chief of staff Lt. Gen. Gabi Ashkenazi. The orders came a day after rockets claimed their second victim inside a week in the southern town of Sderot, a frequent target and Peretz' home town.

A further eight rockets struck southern Israel on Monday, slightly injuring one person. One fell as Peretz, the leader of the Labor Party, voted there in party primaries.

"If there is an answer to terror, it is that the state of Israel is living and breathing, and in Sderot there are elections," Peretz said. "Despite everything, Sderot residents will prove that Hamas does not frighten them and will come to vote at the polling booths."

The outcome of the party race could erode the stability of Olmert's coalition government and determine the embattled prime minister's future. Peretz is predicted to lose and both front-runners have said they would work to topple Olmert.

Israel's air campaign against Palestinian militants entered its 12th day on Monday. About 50 Palestinians, most of them militants, have died in the attacks.

A Hamas official said a delegation from the organization's Syria-based political bureau, would head to Cairo on Tuesday to discuss a possible new truce with Israel as well as a halt to Palestinian infighting.

Israel's Gaza airstrikes have bruised Hamas, knocking out key bases, killing several military commanders and forcing the movement's leadership underground. Israel has so far avoided attacks on the political leadership of Hamas, which is the senior partner in the Palestinian coalition government.

Missiles have hit near the homes of Haniyeh and Hamas lawmaker Khalil al-Haya, but the army has said they were not targets.

Haniyeh has kept out of sight since the attack Thursday on the Shati refugee camp where he lives and did not show up to chair Monday's Cabinet session.

"Ismail Haniyeh did not attend the meeting for security reasons," Palestinian Information Minister Mustafa Barghouti said.

Israel's air campaign against Gaza rocket squads coincided with a lull after more than a week of deadly fighting between Hamas and Abbas' Fatah, the two groups that nominally share power in the Palestinian government.

On Monday, Hamas and Fatah loyalists traded fire over a stolen jeep in Shati and fighters on both sides briefly put up roadblocks in and around nearby Gaza City in an effort to find their rivals, until officials of the two groups ordered the checkpoints dismantled in an attempt to ratchet down the tensions.

In the West Bank, Israeli soldiers and security agents seized a Palestinian in the town of Ramallah, who the army said it had been seeking for years for attacks on Israelis, including the December 2000 killing of the son and daughter-in-law of the assassinated anti-Arab leader Rabbi Meir Kahane.

The army named the man as Khaled Shweish, of Fatah.

Complete coverage is available in FOXNews.com's Mideast Center.