A cease-fire between Israel and Palestinian militant groups might be reached Tuesday, according to an Egyptian security source, amid intensified international efforts to mediate a quick end to the escalating violence now in its seventh day.

The informed source said the Egypt-brokered deal would require Israel and the militant groups led by Islamic Hamas movement to halt all sorts of cross-border violence for one day or two before discussing each side's conditions. Hamas and Israel will hold internal meetings before informing the Egyptian side with their conclusions. Both sides have reached an initial agreement to calm the situation.

However, Hamas officials in Gaza refused to comment on the issue at present. Chief of the Hamas politburo Khaled Meshaal said Monday the Islamic group wants to reach a truce with Israel, but stressed whoever started the war must stop it, and the war must stop"under our conditions prior to the one who started it."

A 60-member delegation of Egyptian political powers, led by chairman of the Freedom and Justice Party Mohamed Saad al-Katatni, arrived Monday in Gaza.

Egyptian Foreign Minister Mohamed Amr said Egypt is keeping communication with the Israeli side on the truce bid, and the results could be seen within days."We will see the results of these efforts in the coming period," Amr noted.

Israel launched a military offensive in Gaza on Wednesday, killing 110 Palestinians and wounding more than 800 so far. Responding to the attacks, Hamas and other Palestinian groups fired hundreds of missiles and rockets into Israel, reaching the outskirts of Jerusalem and Tel Aviv and killing three Israelis.

UN Secretary-General Ban Ki-moon arrived Monday evening in Cairo for a two-day visit to push for an early ceasefire between Israel and the Palestinian militants in the Gaza Strip. He will leave for Israel on Tuesday to convey this stance to the Israeli side.

On the same day, the UN Security Council wrapped up a closed-door meeting on the Israeli raids on the Gaza Strip, but still has to finalize a proposed press statement on the issue.

The council is expected to meet again Tuesday morning with the hope to adopt the statement on the issue, said Hardeep Singh Puri, the Indian UN ambassador who holds the rotating council presidency for November.

"Yes, we have been working on that draft press statement," Puri said."There's still working progress...We hope that we can continue this work first thing tomorrow morning."

The council began its closed-door meeting on 6:30 p.m. EST(2330GMT) on Monday to consider a draft statement proposed last Thursday by Morocco, the only representative of Arab countries on the Security Council, to call for a halt to the Israel-Hamas hostilities.

Earlier on Monday, the Russian permanent representative to the United Nations Vitaly Churkin accused the United States of attempting to"filibuster" a statement of the Security Council on Gaza.

"To me, it unfortunately looked like a little bit of a filibuster attempt," Churkin told reporters.

Also on Monday, U.S. President Barack Obama called Egyptian President Mohammed Morsi and Israeli Prime Minister Benjamin Netanyahu respectively to discuss the ongoing violence in Gaza.

Obama, who is on an Asian tour, discussed with Morsi ways to"de-escalate the situation in Gaza," and underscored the"necessity" of Hamas ending rocket fire into Israel.

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