Hamas has previously said it is open to a short extension to complete talks on Phase 2, but that was before Israel held up the release of the prisoners.
One of the Egyptian officials said Egypt is also demanding Israel complete its withdrawal from the Philadelphi corridor, on the Gaza side of the border with Egypt, before moving on to the next phase.
But Egypt, which has served as a key mediator, has refused to discuss an extension of Phase 1 until negotiations over Phase 2 begin, according to two Egyptian officials who were not authorised to brief reporters and spoke on condition of anonymity.
In exchange, Hamas sought the release of more Palestinian prisoners, a lasting ceasefire, and a complete Israeli withdrawal from the Gaza Strip.
The second phase was always going to be the most difficult because it would likely force Israel to choose between its two main war goals — the safe return of the hostages and the annihilation of their captors.