US President Donald Trump's special envoy, Steve Witkoff, is to meet officials from Qatar, Egypt and Turkey in Florida, hoping to salvage efforts to reach the second stage of the deal.
"Our people expect these talks to result in an agreement to put an end to ongoing Israeli lawlessness, halt all violations and compel the occupation to abide by the Sharm El-Sheikh agreement," Hamas political bureau member, Bassem Naim, told AFP.
During the second stage, Israel is supposed to withdraw from its positions in Gaza, an interim authority is to govern the Palestinian territory instead of Hamas, and an international stabilisation force is to be deployed.
Israel and Hamas backed the agreement, which was brokered by Washington and its regional allies, in October, but progress has been slow.
The ceasefire also remains fragile with both sides alleging violations, and mediators fearing that Israel and Hamas alike are stalling.
The health ministry in Hamas-run Gaza said on Thursday that at least 395 Palestinians have been killed by Israeli fire in the territory since the ceasefire came into effect on October 10.
Israel has also repeatedly accused Hamas of violating the ceasefire, with the Israeli military reporting three soldiers killed in the territory since the truce entered into force.
Egypt, a key mediator between Israel and Hamas, said it was pushing for a swift implementation of the second phase of the ceasefire deal.
Egyptian Foreign Minister Badr Abdelatty said that, while swift implementation was essential to realising all elements of the deal, steps must be taken to halt truce violations.
The international community must "exert real and effective pressure to halt all violations that occur on a daily basis of the ceasefire agreement," he told a news conference in Cairo.
Naim said the new talks should also boost entry of humanitarian aid into Gaza.
He said talks should address how to implement the plan in way to ensure "sustainable stability, launches a comprehensive reconstruction process and paves the way for a political track enabling Palestinians to govern themselves, culminating in a fully sovereign and independent state".
In the first phase of the deal, Palestinian militants committed to releasing the remaining 48 living and dead captives held in the territory. To date, they have released all of the hostages except for one body.
But the Trump administration is now keen to proceed to the difficult second stage, with the provision for Hamas to lay down its weapons being a particular sticking point.
Hamas's Gaza chief Khalil al-Hayya said Sunday that the militant group had a "legitimate right" to hold weapons. Israel has repeatedly insisted Hamas will be disarmed.
The ceasefire's third phase includes plans for the reconstruction of the vast areas of Gaza levelled by Israel's retaliatory military campaign for Hamas's October 2023 attack on Israel.
