Egyptian mediators began separate talks on Monday with Hamas and with Israel to flesh out details of a ceasefire 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 unable 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.
A day later Israeli troops avoided interfering when Gaza farmers neared the fence to tend to their land, and Israel also eased its restrictions at sea, permitting Gaza fishermen to head farther away from the coast than in the past three years.
Israel launched its air offensive against the Gaza Strip on November 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.
U.N. Secretary-General Ban Ki-moon told an Austrian newspaper in remarks due for publication on Tuesday that "the most important thing right now is ensuring that there are no illegal deliveries of rockets and weapons to Hamas" and "free access and freedom of movement in Gaza".
Ban thought the Gaza crisis also showed "the status quo is no option" and urged a resumption of Israeli-Palestinian peace talks stalled since 2010, though Hamas has had no role in those negotiations as it rejects any recognition of Israel.
(Reporting by Nidal Almughrabi; Additional reporting by Michael Shields, in Vienna; Editing by Alison Williams)