Gaza ceasefire talks restarted on Monday in Cairo and Doha with an Israeli delegation meeting Egyptian mediators to discuss the latest demands, after a months-long lull in negotiations in the nine-month-old war.
There is renewed hope for a breakthrough amid months of disagreements between the two warring parties after Israeli Prime Minister Benjamin Netanyahu announced on Sunday a response to a proposal from the Palestinians last week.
The talks this week will focus on an Israeli proposal which includes details on the release of hostages in Gaza, and security issues related to the Egypt-Gaza border - known by Israel as the Philadelphi corridor - amid concerns of weapons smuggling.
Netanyahu presented a list of "non-negotiable" demands, including crucially that Israel could resume fighting in Gaza - a point which Palestinians previously opposed.
On Sunday, however, a Hamas official indicated that the group has now watered down its previous condition.
A senior Hamas official told news agency AFP that the group was ready to discuss a deal which did not need a commitment by Israel for "a complete and permanent ceasefire".
"Hamas had previously required that Israel agree to a complete and permanent ceasefire," the official told AFP.
"This step was bypassed, as the mediators pledged that as long as the prisoner negotiations continued, the ceasefire would continue."
Netanyahu's list of four demands includes blocking any weapons smuggling from Egypt into Gaza and "the return of thousands of armed terrorists to the north of the Gaza Strip".
It also stipulates that "Israel will return as many live hostages as possible", referring to the captives taken by armed Palestinian groups on 7 October.
Some 116 people are still believed to be held in Gaza, though the Israeli army estimates that 42 of them are dead.
Hamas said on Saturday the deal must include an exchange of Israeli captives for Palestinians imprisoned in Israel, and a push for the entry of 400 aid trucks each day into the besieged enclave amid shortages of food, water and medicines.
US President Joe Biden is said to be supportive of Israel's proposal which comes six weeks after the president, in an unusual move, publicly announced a plan for Israel and Hamas on 31 May, but failed to get the deal over the line.
Israel's plan includes a starting point six-week pause in fighting which would see the Israeli military withdraw from populated areas of the Gaza Strip during which period the captives would be exchanged.
The head of the US Central Intelligence Agency William Burns is expected in Doha and Cairo this week, Reuters reported while Turkey and Egypt will engage in efforts to secure an agreement between Hamas officials and Israel.
In Doha, Burns will meet with the Egyptian intelligence head and the Qatari Prime Minister Mohammed bin Abdulrahman Al-Thani, Israeli media reported.
Netanyahu has been facing increasing pressure from the Israeli public in recent weeks. Thousands of people took to the streets of Tel Aviv over the weekend in mass demonstrations calling for the safe return of the hostages.
The leader has been accused of prioritising his own war objectives and political career over that of the Israeli citizens in Gaza.
Meanwhile, Israel's relentless bombardment of the dense enclave has killed more than 38,000 Palestinians, left over 87,000 wounded and displaced 90 percent of the population, prompting a major humanitarian crisis.