Hamas said there were "positive indicators" for the start of the ceasefire's second-phase talks but did not elaborate.
Israel said it would send a delegation to Qatar's Doha on Monday to advance negotiations after accepting an invitation from mediators.
A delegation from Hamas is engaging in ceasefire talks in Cairo with Egyptian mediators who have been helping facilitate the talks along with officials from Qatar.
They aim to proceed to the next stage of the deal, which could open the way to ending the war.
"We affirm our readiness to engage in the second-phase negotiations in a way that meets the demands of our people, and we call for intensified efforts to aid the Gaza Strip and lift the blockade on our suffering people," Hamas spokesman, Abdel-Latif Al-Qanoua, said in a statement on Saturday.
Israeli Prime Minister Benjamin Netanyahu's office said: "Israel has accepted the invitation of the mediators backed by the US, and will send a delegation to Doha on Monday in an effort to advance the negotiations."
As diplomacy continues, an Israeli airstrike killed two Palestinians in Rafah in southern Gaza on Saturday, medical sources said.
The Israeli military said its aircraft struck a drone that crossed from Israel into southern Gaza and "several suspects" who tried to collect it in what appeared to be a botched smuggling attempt.
The strike came one day after an Israeli drone strike killed two people in Gaza on Friday.
The Israeli military said it attacked a group of suspected militants operating near its troops in northern Gaza and planting an explosive device in the ground.
The Gaza ceasefire deal that took effect in January calls for the remaining 59 hostages in Hamas captivity to be freed in a second phase, during which final plans would be negotiated for an end to the war.
The first phase of the ceasefire ended last week, and Israel has since imposed a total blockade on all goods entering the enclave, demanding that Hamas free remaining hostages without beginning the negotiations to end the Gaza war.
Fighting has been halted since January 19 and Hamas has released 33 Israeli hostages and five Thais for some 2000 Palestinian prisoners and detainees. Israeli authorities believe fewer than half of the remaining 59 hostages are still alive.
Israel's assault on the enclave has killed more than 48,000 Palestinians, according to Gaza health authorities.
It has also internally displaced nearly Gaza's entire population and led to accusations of genocide and war crimes that Israel denies.
The assault began after Hamas-led Islamist fighters raided southern Israel on October 7, 2023, killing around 1200 people and taking 251 hostages, according to Israeli tallies.
with EFE
