(Reuters) - Gaza truce talks were underway in Paris on Friday, in what appears to be the most serious push for weeks to halt the fighting in the battered Palestinian enclave and see Israeli and foreign hostages released.

A source briefed on the ceasefire talks, who could not be identified by name or nationality, said talks had begun with Israel's head of Mossad intelligence service meeting separately with each party - Qatar, Egypt and United States.

"There are budding signs of optimism about being able to move forward toward the start of a serious negotiation," the source said. Egypt's Al Qahera TV News also reported that the talks had begun.

An official from Hamas said the militant group had wrapped up ceasefire talks in Cairo and was now waiting to see what mediators bring back from the weekend talks with Israel.

Mediators have ramped up efforts to secure a ceasefire in Gaza, in the hope of heading off an Israeli assault on the Gaza city of Rafah where more than a million displaced people are sheltering at the southern edge of the enclave.

Israel says it will attack the city if no truce agreement is reached soon. Washington has called on its close ally not to do so, warning of vast civilian casualties if an assault on the city goes ahead.

Hamas leader Ismail Haniyeh met Egyptian mediators in Cairo to discuss a truce this past week on his first visit since December.

Two Egyptian security sources earlier confirmed that Egyptian intelligence chief Abbas Kamel would head on Friday to Paris for the talks with the Israelis, after wrapping up talks with Haniyeh on Thursday. Israel has not publicly commented on the Paris talks, which are expected to continue through the weekend.

The Hamas official, who asked not to be identified, said the militant group did not offer any new proposal at the talks with the Egyptians, but was waiting to see what the mediators would bring back from their talks with the Israelis.

"We discussed our proposal with them (the Egyptians) and we are going to wait until they return from Paris," the Hamas official said.