Live updates: Follow the latest news on Israel-Palestine
Talks on a potential prisoner exchange with Israel have begun, a senior Hamas official confirmed to The National but stressed it was too early to reach a deal that would lead to a decrease in hostilities.
Qatar has been in touch with Hamas officials in Doha and Gaza, according to reports.
The potential deal would result in the release of Israeli prisoners taken hostage on Saturday, in exchange for the freedom of female Palestinian political prisoners.
Details about negotiations focusing on the release of 36 Palestinians from Israeli jails have not previously been reported.
“I think we are not talking about one country leading the efforts on mediation between Hamas and Israel, but I can say that talks have indeed begun since yesterday,” said Osama Hamdan, Hamas's top representative in Lebanon and member of the group’s political office.
Sources from Hamas confirmed that Qatar had begun mediation talks with Hamas on a potential deal that could see them exchange female Israeli prisoners for the release of female Palestinian prisoners.
Qatar and Egypt appear to be leading the efforts to reach an immediate ceasefire with the Palestinian group. Egyptian officials told The National that Egypt's contacts over the past 24 hours included talks with senior EU and US officials, as well as regional heavyweights such as the UAE, Saudi Arabia, Jordan and Qatar.
Defence Minister Yoav Gallant said Israel's blockade would be tightened to prevent food and fuel from being brought into the strip, home to 2.3 million people.
Egypt had urged Israel to exercise restraint and Hamas to hold its captives in good condition to keep open the possibility of de-escalation.
The Al Qassam Brigades, the military wing of the Hamas movement, on Saturday launched “Operation Al Aqsa Flood” with rockets targeting enemy sites, airports, and military bases. Its fighters also launched a ground incursion into southern Israel and took dozens of Israeli hostages.
Hamas said it would initially agree to an exchange only if Israel releases all 36 female Palestinians currently in Israeli custody, according to one Hamas source. Eran Lerman, a former Israeli deputy national security adviser, said no Israeli would concede to conditions of the hostage takers, citing the brutality of the attack.
About 50 Israeli hostages are being held by Hamas militants in Beeri Kibbutz near the Gaza border, according to some Israeli reports.
Qatar has yet to publicly acknowledge its role in mediating a prisoner exchange deal. More recently, Qatar played a crucial role when it mediated between Hamas, Egypt and Israel to reopen a main crossing with the Gaza Strip at the end of September.
Gaza's Health Ministry said on Monday that about 493 Palestinians have been killed and 2,751 wounded in Israeli air strikes on the blockaded enclave since Saturday.
For a ceasefire to come into effect, Hamas is calling for an immediate stop to all Israeli settlement expansions and to Israeli aggression at the Al Aqsa mosque.
“In the end, our top priority and demand is for Israel to free all Palestinian prisoners and end Israeli provocations in the occupied West Bank and Jerusalem, particularly Al Aqsa Mosque,” Mr Hamdan said.
Mr Hamdan said hostilities are expected to continue for the foreseeable future given the group’s “armed victory”.
“We have had experience with the occupiers’ wars on Gaza in 2008 and 2014 so for the armed wing of Hamas, the Al Qassam Brigades to be so victorious over the past days gives many in Gaza the will to go on fighting until the end,” he said.
Israel's troops were still fighting to recapture its towns from Hamas fighters on Monday, acknowledging the battle was taking longer than expected more than two days after the militants crossed from Gaza.