Egyptian mediators began separate talks on Monday with Hamas and with Israel to flesh out details of a cease-fire agreed last week that ended eight days of fighting in the Gaza Strip.
An Egyptian official told Reuters the talks would discuss Palestinian demands for the opening of more Israeli crossings into Gaza - a move that would help end six years of blockade of the coastal enclave ruled by the Islamist Hamas.
The Egyptian-brokered ceasefire came into force last Wednesday, ending hostilities between the two sides that cost the lives of 167 Palestinians and six Israelis.
However, the text of the truce stipulated that issues such as access to the borders, free movement for Gazans and the transfer of goods would be dealt with "after 24 hours."
Israel imposed restrictions on Gaza in 2006, following an election victory by Hamas, which refuses to recognize Israel's right to exist. The curbs were tightened, and backed by Egypt, after Hamas seized control of the enclave in a civil war.
Some of the import and export limits have since been eased, but Israel still prevents a long list of goods into the territory - including many items needed for construction - arguing they could be used for the manufacture of weapons.
Senior Hamas leader Mahmoud Al-Zahar told reporters on Saturday that the group wanted to see the opening of all four goods crossings with Israel that used to operate before 2006.
Only one operates at present, with a second passenger terminal reserved for the handful of Palestinians and foreigners who are allowed in and out of the territory.
The Egyptian official said Cairo would also urge both sides to cement their commitments to the ceasefire agreement.
Israeli soldiers shot dead a Palestinian man on Friday after he approached the Gazan "no-go" border area, apparently in the belief that under the terms of the ceasefire deal he was able to go up to the heavily patrolled fence.
Alarmed by the prospect of the truce failing, Egypt encouraged Hamas police to be deployed along the border line to keep Gazans away and prevent further violence.
Israel launched its air offensive against the Gaza Strip on Nov. 14 with the declared aim of deterring Islamist militants from firing rockets into its territory.
The Israeli military also says its soldiers have come under increasing attack from the border area this year, including earlier this month when a jeep was hit by an anti-tank missile.
Meanwhile, Hamas said on Monday it was backing President Mahmoud Abbas's attempt to win more clout for Palestinians at the United Nations, the latest sign of a rapprochement between the political rivals.
The Palestinians are registered as an observer entity at the UN and Abbas wants to see them upgraded to a "non-member state" in a UN General Assembly vote on Nov. 29, giving him access to other international organizations.
The decision by Hamas was unexpected. It does not recognize Israel's right to exist and has dismissed previous attempts by Abbas to promote the Palestinian cause on the diplomatic stage.
After more than five years of deep divisions, the two main political forces in the Palestinian territories have shown signs this past week they were ready to resume unity talks - driven closer together by the Israeli assault on Gaza.
Hamas spokesman Sami Abu Zuhri said the group backed any political gain Abbas could achieve at the United Nations "without causing any harm to the national Palestinian rights".
Hamas political chief Khaled Meshaal, who lives in exile, told Abbas by telephone of his movement's change of heart, Hamas said in a statement.
Direct peace talks between Israel and Abbas broke down in 2010 over the question of Israeli settlement building in the West Bank and East Jerusalem -- land the Palestinians want for their future state.
Hamas might struggle to explain its new position to some of its hardline supporters. As recently as Saturday, senior Hamas leader Mahmoud al-Zahar had urged Abbas not to go to New York.
Abbas's UN initiative "represents an... official concession of the 1948 land," Zahar told reporters, referring to the year Israel proclaimed its independence following the end of British rule in the region.
While Hamas leaders accept the notion of a Palestinian state along lines established before the 1967 Middle East War, they say this should only be a transitional solution ahead of the eventual creation of a nation on the basis of 1948 boundaries.
Abbas has said he supports a two-state solution on the basis of the 1967 lines.
In his conversation with Abbas, Meshaal stressed the need for reconciliation between the two factions, especially in the wake of the Israeli offensive, which was ended thanks to a ceasefire deal brokered by Egypt.
"This signals that Hamas is showing greater flexibility towards reconciliation than any time before," said Gaza political analyst Hani Habib.
Speaking to hundreds of supporters in the West Bank city of Ramallah on Sunday, Abbas vowed he would speed up unity efforts after he returns from the UN vote.
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