An delegation is to travel to at the end of this week to explore the possibility of a renewed truce with militant group .
They travel on behalf of the National Security Council and new Prime Minister Naftali Bennett's office, Israel's Army Radio revealed on Thursday.
The station said the new government - headed by the far-right premier - had previously sent messages to Cairo explaining that it wanted a de-escalation with Hamas, which rules Gaza.
after the so-called won a key confidence vote on Sunday in the Knesset.
In doing so, they deposed who had held the position for 12 years.
Army Radio said the Israeli representatives will explore several themes with the Egyptians, including Gaza reconstruction and Israeli prisoners held by Hamas.
The Bennett government maintains that it will not permit rebuilding efforts in Gaza until the prisoner issue is resolved.
Analysts say there are significant rifts between the two parties on prisoner exchange, plus the conflation of this issue and rebuilding efforts.
The Israelis are to relay via Egypt that they do not seek to inflame the situation, after recent flare-ups in tensions.
Though suggestions of military force have been made, some within the military establishment are seeking to deescalate by boosting the enclave's economic fortunes, the Israeli Walla outlet reported on Thursday.
Israel on Wednesday morning, during the first escalation since an Egyptian-brokered ceasefire in May, as fire balloons were launched from the enclave.
The overall Israeli military consensus is that the launch of the balloons is due to Palestinian economic suffering, Walla said.
The has been .
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The quantities and types of items allowed to enter the enclave are tightly controlled by Israel, meaning there are serious availability problems even for essentials like food, fuel and medicine.
This latest Israeli bombing follows May's against Gaza.
In that time, 260 Palestinians were killed.
In Israel, rocket fire from Gaza militant groups caused 13 deaths.