Egyptian officials mediating talks for a durable truce in Gaza met an Israel delegation during the night and were to relay their demands to Palestinian representatives, Palestinian sources say.
The shuttle diplomacy comes as a fragile ceasefire in the Gaza Strip after a month of fighting between Hamas and Israeli forces entered a second day on Wednesday.
Palestinian officials in Cairo said they would respond to the Israeli terms through the Egyptian intelligence officials, although a senior Hamas official has already rejected an Israeli demand that militants in Gaza disarm.
Meanwhile international Middle East peace envoy Tony Blair and UN Middle East peace process coordinator Robert Serry were scheduled to hold talks with Egyptian officials later on Wednesday.
The Egyptian-mediated 72-hour ceasefire that went into effect on Tuesday has brought relief to both sides after fighting that erupted on July 8 killed 1875 Palestinians and 67 people on the Israeli side.
The talks in Cairo are aimed at securing a durable ceasefire after the three-day window closes.
Experts say the underlying problems in Gaza, a small coastal enclave flanked by Israel and Egypt that has undergone three conflicts with Israel since 2008, would also have to be addressed.
US Secretary of State John Kerry, in a BBC interview, called for a sustained ceasefire but stressed that the crucial wider issues would need to be tackled.
The Palestinians demand an end to the eight-year Israeli blockade of Gaza and the release of Palestinian prisoners.
Israel has demanded that Hamas, which won Palestinian elections in 2006 although designated a terrorist group by the United States and Israel, disarm its militia.
A senior Hamas official in Cairo said on Tuesday the militants would not even consider laying down their weapons, which include an arsenal of unguided rockets and anti-tank missiles.
"Whoever tries to take our weapons, we will take his life," said Ezzat al-Rishq on Twitter.
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