JERUSALEM/GAZA - Israel and Hamas have reached an agreement to release the remaining six living hostages held in Gaza included in the first phase of the ongoing ceasefire deal on Saturday, Israeli Prime Minister Benjamin Netanyahu's office said on Tuesday.

The office said in a statement that the new "understanding" was achieved following talks in Egypt's capital Cairo.

A well-informed Egyptian source told Egypt's state-affiliated Al-Qahera News TV channel that the achievement came following successful talks in Cairo between Egyptian, Qatari, Israeli, and U.S. delegations.

Citing an Israeli official, Israel's state-owned Kan TV News reported that in exchange, Israel agreed to allow shelters, trailers, and heavy equipment for the reconstruction of Gaza to enter the devastated enclave.

In addition, Hamas would return the bodies of four hostages on Thursday and four additional bodies next week, Netanyahu's office said.

Khalil al-Hayya, a senior Hamas official and chief Hamas negotiator, confirmed in a televised address that four bodies would be transferred on Thursday. He added that Hamas would also free six Israeli hostages as part of the exchange for Palestinian detainees.

Under the original terms of the ceasefire deal, Hamas was supposed to release three living hostages on Saturday and another three the following Saturday, in exchange for hundreds of Palestinian detainees.

However, amid pressure from Israel, backed by the United States, and following negotiations with Qatari and Egyptian mediators, all six hostages will be freed on Saturday.