CIA Director Mr George Tenet pressed ahead today with US efforts to broker a lasting ceasefire between Israel and the Palestinians, bringing together security chiefs from both sides.
Senior Israeli political sources said the talks in Jerusalem began around 8 p.m. (17:00 GMT).
But sharp differences over the shape of a truce threatened to scuttle the effort and fresh violence fuelled tensions.
A suspected car bomb seriously wounded a member of the Palestinian militant group Islamic Jihad in the West Bank and a baby of Jewish settlers died six days after being hit by stones that Palestinians threw at his parents' car.
Israeli officials said they were not optimistic about chances for a breakthrough at the security talks.
The two sides exchanged accusations despite a fragile ceasefire that has reduced but not ended eight months of violence. Almost 600 people have been killed since Palestinians launched an uprising against Israeli occupation.
A Palestinian official told Reuters: "[Israeli Prime Minister Ariel] Sharon wants to complicate the ceasefire because he does not want to implement other political issues such as outstanding redeployments and halting all settlement activities."
The official said the Palestinians replied in writing to Mr Tenet's proposals, reiterating the security agreement must be part of a package and not separate from a political accord.
Mr Sharon’s adviser Mr Raanan Gissin said Israel's patience was wearing thin.
"We instituted a unilateral ceasefire on May 22nd and since then we have just been bleeding. [Palestinian President Yasser] Arafat is working on borrowed time," he said.
Israel has said violence must stop before the implementation of a cooling-off period and confidence-building moves proposed by a committee led by former US Senator George Mitchell.