Palestinian Hamas activists take part in an anti-Israel rally organized by the Hamas movement in Gaza March 7, 2008.

JERUSALEM (Reuters) - Israel and Hamas Islamists who control the Gaza Strip have both been holding their fire across the tense border as Egypt tries to mediate a truce, officials from both sides said on Monday.

Israeli Prime Minister Ehud Olmert denied any agreement to halt military action against militants in the coastal enclave, but Palestinian President Mahmoud Abbas said he believed Israel would go along with a deal.

Abbas said Hamas and Islamic Jihad, the main groups in Gaza behind cross-border rocket fire at Israel, want assurances their leaders will not be attacked by the Jewish state.

A Gaza truce sought by the Palestinian president could be key to U.S.-brokered peace efforts but likewise benefit Hamas, which seized the coastal enclave in June after routing Abbas's more secular Fatah forces.

Israel has not struck in the Gaza Strip since Thursday, three days after it ended an offensive that killed 120 Palestinians.

The number of Palestinian rocket attacks on southern Israel has also dropped sharply since Olmert said last Wednesday Israeli forces would have no reason to attack Gaza if the daily salvoes stopped.

Hamas's armed wing has not itself claimed responsibility for firing any rockets since Israel wrapped up its ground and air assault. In the absence of Israeli "aggression", Hamas official Sami Abu Zuhri said the group had no cause to launch them.

"It seems that Hamas has decided for now not to shoot. And we're not shooting either," said an Israeli official, who declined to be named because of the sensitivity of the issue.

"This could well become a ceasefire. But the ball is in Hamas's court," the official said.

In new public comments on the lull, Olmert insisted Israel was not negotiating with Hamas "directly or indirectly". But in a nod to a possible de facto truce, he repeated that if rockets were not fired at Israel, "we will have no reason to shoot".

Speaking in Amman, Abbas said: "Hamas and Islamic Jihad have asked that their leaders should be protected from Israeli (attack). I think the Israelis are agreeing to this or have agreed. We may be hearing about this deal in the coming few days."

Israel, the United States and the European Union refuse to talk with Hamas, which opposes the peace talks, until it recognizes Israel and renounces violence.

BLOODSHED

The recent fighting along the Israel-Gaza frontier and longer-range rocket salvoes that hit a major southern Israeli city had threatened to derail the statehood talks.

In protest at the bloodshed in Gaza, Abbas briefly suspended the negotiations. They are due to resume later this week.

Egypt held inconclusive meetings on Thursday with leaders of Hamas and another militant group, Islamic Jihad. A senior Israeli defense official, Amos Gilad, visited Cairo over the weekend.

Over the past three days, Gaza militants from various factions have launched four rockets and 10 mortar bombs across the frontier, the Israeli military said, compared with about 10 to 15 rockets a day a week earlier.

"The efforts by Egypt are highly appreciated," said Ismail Haniyeh, prime minister of Hamas's government in the Gaza Strip. He called the pause in Israeli attacks in Gaza a sign of "U.S. and Israeli recognition that our people are unbreakable".

An Israeli political source said there had been "an exchange of ideas" between Israel and Hamas via Egyptian mediators. The source did not elaborate.

The political source said Olmert was keen to calm violence with Hamas so that talks with Abbas could make progress and enable him to present a viable peace platform to voters should the statehood moves force a new Israeli election.

Amid much skepticism, Washington has said it hopes to achieve a deal before year's end on Palestinian statehood.

For Hamas, a ceasefire would be particularly attractive if it included an easing of an Israeli-led Gaza blockade. Israeli generals, however, are concerned Hamas might use a lull to regroup and rearm after last week's punishing Israeli offensive.

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