Israel's "new" conditions include keeping troops inside Gaza along its border with Egypt, an informed source said, while Hamas demands "a complete ceasefire, a complete withdrawal from the Strip, a normal return of the displaced and a (prisoner) exchange deal" without restrictions.

Israel also demanded veto rights on the prisoners to be exchanged, and the ability to deport some prisoners rather than send them back to Gaza, the source said.

Separately, Israeli Defence Minister Yoav Gallant spoke to his US counterpart Lloyd Austin Friday, stressing the importance of negotiating the release of the hostages held in Gaza since October 7.

Gallant "highlighted that the achievement of this agreement is both a moral imperative and a strategic, security priority", his office said in a statement.

Hamas militants seized 251 people during the Palestinian Islamist movement's unprecedented attack on October 7, 111 of whom are still held in Gaza, including 39 the military says are dead.

Israel's retaliatory military offensive has killed at least 40,005 people in Gaza, according to the Hamas-run territory's health ministry, which does not provide a breakdown of civilian and militant deaths.