An anonymous and high-ranking Hamas representative tells AFP that the Islamist movement has sent a delegation to Cairo.
The delegation will meet with Egyptian representatives to discuss new ideas aimed at achieving a ceasefire, the person says.
Hamas rejected an offer from Israel last week, citing demands that the movement be completely disarmed without sufficient guarantees that Israel's military operations would cease.
An Israeli delegation traveled to Cairo on Sunday evening, reported Qatari media.
Hostages and Prisoners
An anonymous Palestinian source with insight into the negotiating situation tells British BBC that the Egyptian and Qatari mediators have presented a new framework. It outlines a path towards a ceasefire that would last for five to seven years, where all hostages held in Gaza would be released, Palestinian prisoners in Israel would also be released, and Israel would make a complete military withdrawal from the Gaza Strip.
Over the weekend, Israel's Prime Minister announced an escalation of the war, promising that it would not end until Hamas had been destroyed and all hostages had been returned. Critics at home see this as two goals that cannot be combined, and large demonstrations were held in Israel over the weekend.
According to BBC's source, Hamas has shown signs of being willing to hand over control of Gaza to another Palestinian entity. However, Israel's Netanyahu has ruled out allowing the Palestinian Authority, which leads the self-government on the occupied West Bank, to be involved in governing.
Extreme Partner Demands
Behind Israel's Prime Minister Netanyahu stands his ultra-nationalist government partner with sharp demands.
Finance Minister Bezalel Smotrich, whose support Netanyahu needs, said on Monday that he correctly questioned the previously agreed-upon ceasefire, seeing it as inevitable that Israel would have to "subdue, defeat, and destroy Hamas, conquer the Gaza Strip, and establish military rule" in Gaza.
I think it's time to go on the offensive in Gaza. If it doesn't happen, then this government has no raison d'être, the minister said in a TV interview, according to reports in other Israeli media.