GAZA - Israel and the Gaza Strip's Hamas rulers signaled on Sunday they were looking to end a flare-up in violence that began four days ago with a missile attack on an Israeli school bus and has claimed the lives of 19 Palestinians.

A Palestinian official close to UN- and Egyptian-mediated negotiations said Israel and militant groups in Gaza had agreed terms for a truce to end four days of cross-border violence in which 19 Palestinian militants and civilians were killed.

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"Palestinian factions have agreed to halt rocket fire and Israel agreed to cease attacks on the Gaza Strip," the official said.

Israel had no immediate comment, but a senior official suggested a tacit deal may have been reached.

"What happens from here on is up to the other side," the Israeli official told reporters in Tel Aviv, speaking on condition of anonymity. "It seems calmer now, but it is still not clear where this is going."

"We will judge the other side over the next few days. The extent to which Hamas controls the other militant groups will affect the way we choose to act," the Israeli official added.

Israeli Defense Minister Ehud Barak said earlier Hamas had already been hit hard and a ceasefire might be the way to go.

"If they stop firing on our communities, we will stop firing. If they stop firing in general, it will be quiet, it will be good," Barak said on Israel Radio.

The fighting since Hamas militants fired an anti-tank rocket at an Israeli school bus, critically injuring a teenager, has stoked fears of a larger escalation that could include an Israeli ground incursion in Gaza reminiscent of the war in 2008.

Despite behind-the-scenes intervention by Egypt and a UN envoy in search of a ceasefire, militants fired at least eight rockets at Israel on Sunday, in addition to more than 120 in the previous two days, Israeli police and military officials said.

There were no reported Israeli air strikes on Gaza on Sunday.

Israeli Prime Minister Benjamin Netanyahu said Israel would raise the stakes if cross-border attacks continued.

"Our policy is clear, if the attacks continue on Israel's citizens and soldiers, the response will be much harsher," Netanyahu said at the start of a weekly cabinet meeting.

Abu Ahmed, a spokesman for Islamic Jihad, a group that fires rockets at Israel, said in a statement the group "have agreed to the Arab and European proposal for calm for the sake of the interests of our people", but would respond to further Israeli fire.

Hamas said it, too, did not want a further escalation but stopped short of saying it had agreed to a truce.

"If the Israeli aggression stopped, it would be natural for calm to be restored," Hamas spokesman Sami Abu Zuhri said. "Calm will be met with calm."

Reuters