Hamas said on Saturday it will study an Israeli response to the group's proposal for a ceasefire in Gaza.
A delegation from mediator Egypt arrived in Israel on Friday to jump-start stalled negotiations.
“Hamas has received the [Israeli] response to the movement's position that was handed over to Egyptian and Qatari mediators on April 13,” Hamas's deputy head Khalil Al Hayya said.
“Hamas will submit a response to the proposal once it has finished studying it.”
Egypt, Qatar and the US have been trying to secure a truce in Gaza since a week-long halt to the fighting in November enabled the exchange of 80 Israeli hostages for 240 Palestinian detainees.
Israel's war cabinet had discussed a new plan for a truce and hostage release ahead of the Egyptian delegation's visit, agencies reported.
The US has been seeking a temporary ceasefire in Gaza that would see Hamas release female, wounded, elderly and sick hostages in exchange for the release of Palestinian detainees and the delivery of humanitarian aid into the war-torn territory.
The war has killed more than 34,350 people in the Palestinian enclave, according to Gaza's Health Ministry, but negotiations remain deadlocked.
Hamas is sticking to its demands that any agreement must end the war, with Israeli troops withdrawing from Gaza.
The high-level delegation from Egypt sought to push through a ceasefire agreement with Hamas and avert an Israeli offensive on Gaza’s town of Rafah – on the border with Egypt – which Cairo warned could ruin regional stability, officials said.
Egypt’s top intelligence official, Abbas Kamel, led the delegation and planned to discuss with Israel a “new vision” for a prolonged ceasefire in Gaza, an Egyptian official said.
Citing two Israeli officials, Axios reported that Israel told the Egyptian mediators on Friday that it was ready to give “one last chance” to reach a deal on hostages with Hamas before moving forward with an invasion of Rafah.
Rafah is the last refuge for about a million Palestinians who fled Israeli forces further north in Gaza earlier in the war – nearly half of Gaza's population of 2.3 million.
The Israeli military has massed dozens of tanks and armoured vehicles in the area in what appears to be preparations for an invasion of the city.
On Thursday, the US and 17 other countries in a joint statement appealed to Hamas to release all of its hostages as a pathway to end the crisis.
Hamas has criticised the US-led move for failing to call for a prolonged ceasefire and the withdrawal of Israeli troops from the Gaza Strip.
However, it said it was “open to any ideas or proposals that take into account the needs and rights of our people”.
White House national security adviser Jake Sullivan said on Friday he saw fresh momentum in talks to end the war and return the remaining hostages.
Hamas fighters stormed into Israeli towns on October 7, killing 1,200 people and capturing 253 hostages.
Israel has set the goal of eliminating Hamas forces from Gaza. The Israelis estimate that 129 hostages are still being held by the Palestinian group, while 34 have died.
Grief as loved ones found at mass grave in Gaza
Rafah attack
Meanwhile, at least six Palestinians died and several were wounded in an Israeli air strike on a house in Rafah, in the south of the Gaza Strip, on Saturday.
Separately, eight people, including children and women, were killed and dozens injured in Israeli air strikes on two homes in the Nuseirat camp in the central Gaza Strip, the Palestinian Wafa news agency reported.
In the West Bank, Israeli forces shot dead two Palestinian gunmen who fired at a checkpoint west of city of Jenin in the occupied West Bank overnight, the Israeli army said.
"Soldiers identified a number of terrorists that arrived by vehicle to the Salem military post and fired toward it," the army said. It often describes gunmen as terrorists.
It added that the soldiers killed two gunmen and confiscated the two M16 rifles used to carry out the attack.
Wafa confirmed the death of two people and said two others were wounded after Israeli forces opened fire at them near the checkpoint.
In Lebanon, an Israeli strike in the Beqaa region killed two members of Lebanese militant group Jamaa Al Islamiya, which has fired rockets across the southern border at Israel.
Israel's military said on Friday its air force “struck and eliminated Mosab Khalaf in the area of Meidoun in Lebanon,” saying he was a member of the group.
Jamaa Al Islamiya said two of its field commanders – Khalaf and one of his relatives – were killed in the strike.
Separately, Hezbollah and Israel have been trading fire across Lebanon's southern border. An Israeli strike killed two Hezbollah fighters on Friday, security sources in Lebanon said.
More than 250 Hezbollah members and more than 70 civilians have been killed in Israeli strikes on Lebanon since October. In Israel, missile fire coming from Lebanon has killed around a dozen troops and half as many civilians.
Meanwhile, Yemen's Houthis said on Saturday their missiles hit the Andromeda Star oil tanker in the Red Sea, as they continue attacking commercial ships in the waterway, in a show of support for Palestinians fighting Israel in the Gaza war.
The US Central Command confirmed that Iran-backed Houthis launched three anti-ship ballistic missiles into the Red Sea from Yemen causing minor damage to the Andromeda Star.
