In a press statement issued on Wednesday morning, Egypt's foreign ministry expressed "deep regret" over the resumption of armed confrontations between Palestinian factions and Israel in the warn-torn Gaza Strip.
Cairo warned that the new clashes will "definitely lead to more casualties and injuries among innocent civilians."
"Egypt maintains its bilateral connections with both Palestinian and Israeli sides to urge them accomplish a new ceasefire deal and continue their positive involvement in the negotiations," the statement said, stressing the importance of building on what has been achieved in the indirect talks so far.
"The aim is to open room for reaching a deal that insures a permanent ceasefire and achieves the interest of the Palestinian people, especially in terms of Gaza reconstruction and the opening of crossings."
Israel and Palestinian factions have blamed each other for the collapse of an Egyptian-sponsored 24-hour truce late Tuesday which led to the re-eruption of armed confrontations.
Prior to that, Egypt brokered two 72-hour truce agreements and a five-day ceasefire in a bid to allow more time for negotiators from both sides to reach a common ground.
Israel's Prime Minister Benjamin Netanyahu ordered new airstrikes on Gaza and withdrew his negotiators from the Cairo talks.
Moussa Abu Marzouk, deputy leader of Hamas' political bureau and a member of the Palestinian negotiating team, said on Facebook that Israeli airstrikes had killed the wife and infant daughter of Mohamed Deif, a commander in Hamas' military wing, the Al-Qassam Brigades.
Fatah leader and head of the Palestinian delegation Azzam Al-Ahmed said his team will leave Cairo on Wednesday.
"We are leaving ... but we have not pulled out of negotiations," he told AFP, adding the Palestinians were waiting for Israel to respond to their truce proposal."We will not come back (to Cairo) until Israel responds," he said.
According to the agency, Egypt's ceasefire proposal entails both parties to immediately stop shooting and includes provisions relating to the opening of borders to allow for the free movement of people, goods and construction materials, as well as a clause on regulating the economic crisis in Gaza.
Yet the proposal postpones discussions on a seaport and airport – as well as transferring the remains of two Israeli soldiers for Palestinian prisoners – for another month, until "calm and stability returns."
A member of the Palestinian delegation in Cairo told Ahram Online on Monday that there wasn't much hope in signing a permanent ceasefire between Palestinian factions and Israel.
The source also said that Cairo has exerted great efforts to save the negotiations from what he describes as Israel's inflexibility.
Israel has demanded the disarmament of Palestinian groups since the beginning of the ceasefire talks – which the Palestinian side has persistently refused.
On Wednesday last week, Hamas spokesman Ezzat Al-Rasheq said that Israel "imposed the war on us again."
"We have no choice but to confront and end up being victorious," Al-Rasheq said on Twitter.
The Palestinian ambassador in Egypt previously announced that Palestinian President Mahmoud Abbas will arrive in Cairo on Friday for a two day visit, Al-Ahram's Arabic news website reported earlier this week.
Gamal Al-Shobky, the ambassador, said that Abbas will meet his Egyptian counterpart Abdel-Fattah El-Sisi by Saturday to discuss the latest developments in Cairo's endeavours to finalise a Palestinian-Israeli ceasefire in Gaza.
Al-Shobky, the Palestinian Arab League permanent representative, noted that the bilateral meeting will also discuss a conference for the reconstruction of the war-torn coastal enclave.
Israel's offensive on Gaza, which began on July 8, has killed at least 2,026 Palestinians and led to the deaths of 67 Israelis.