Egypt's intelligence chief met a Palestinian delegation in Cairo, the state news agency Mena said, a day after he conferred with Israeli representatives. The Palestinian team, led by an official from Western-backed President Mahmoud Abbas's Fatah party, includes envoys from Hamas and the Islamic Jihad group.
"The indirect talks between the Palestinians and Israelis are moving forward," one Egyptian official said, making clear that the opposing sides were not meeting face to face. "It is still too early to talk about outcomes but we are optimistic."
Egyptian and Palestinian sources said they expected later on Wednesday an initial response by Israel to Palestinian demands, which it has so far shown no sign of accepting.
Israel withdrew ground forces from the Gaza Strip on Tuesday morning and started a 72-hour Egyptian-brokered ceasefire with Hamas as a first step towards a long-term deal.
In Gaza, where some half-million people have been displaced by a month of bloodshed, some residents left UN shelters to trek back to neighbourhoods where whole blocks have been destroyed by shelling and the smell of decomposing bodies fills the air.
Streets in towns in southern Israel, which had been under daily rocket fire from the Gaza Strip, were filled again with playing children.
The military said that a rocket-warning siren that sounded in the south in the afternoon was a false alarm.