Palestinians dig graves near Gaza
Both sides have agreed to a 12-hour "humanitarian" truce in Gaza that started on Saturday morning, putting a brief stop to a conflict that has killed nearly 1,000 Palestinians -- a large majority of them civilians.
The 19-day Israeli offensive on Hamas-ruled Gaza was launched in response to rockets fired by militants of the Islamist group into the Jewish state, and 37 Israeli soldiers have also died in the violence.
"We all call on parties to extend the humanitarian ceasefire currently in force, by 24 hours that could be renewed," France's Foreign Minister Laurent Fabius told reporters after the meeting, which lasted more than two hours.
"We all want to obtain a lasting ceasefire as quickly as possible that addresses both Israeli requirements in terms of security and Palestinian requirements in terms of socio-economic development."
Kerry and Fabius met with their counterparts from Britain, Germany, Italy, Qatar and Turkey, as well as a representative from the European Union.
"It's now about reaching a common position that we must put an end to the deaths," German Foreign Minister Frank-Walter Steinmeier had said before the talks began.
Kerry, who has been leading international efforts to reach a truce, has been in regular contact with the foreign ministers of Turkey and Qatar as both countries wield influence on Hamas.
Hamas chief Khaled Meshaal is based in Qatar, while Turkey's Islamic-oriented prime minister has strongly criticised Israel's assault on Gaza as well as Egypt's role in trying to clinch a ceasefire.
- Egypt minister absent -
Kerry was in Cairo Friday where he met with his Egyptian counterpart Sameh Shoukri and UN chief Ban Ki-moon, but failed to reach a deal.
The United States and Egypt have been working on a plan that, diplomats say, would provide a seven-day truce during which the two sides would negotiate a longer-term deal.
But while Israel and Hamas agreed to a temporary ceasefire on humanitarian grounds, they have rejected any form of lasting truce.
Hamas wants its Turkish and Qatari allies to be involved in any ceasefire negotiations.
But relations with Egypt are strained over Turkey and Qatar's support for the banned Muslim Brotherhood movement.
Unlike his Islamist predecessor Mohamed Morsi whom he toppled and detained last year, current Egyptian leader Abdel Fattah al-Sisi has sought to isolate the militant Palestinian movement in the neighbouring Gaza Strip.
Egypt's foreign minister was pointedly absent from the Paris meeting, which France dismissed by saying that Egypt was still closely associated with the talks.
Speaking in Cairo Friday after his plan was rejected, Kerry said Israel and Hamas "still have some terminology" to agree to on a ceasefire, but added they had a "fundamental framework" on a truce.
Still, the two sides remain at odds over the shape of a final deal.
Hamas says any truce must include a guaranteed end to Israel's eight-year blockade of Gaza, while in Israel there are calls for any deal to include the demilitarisation of the Gaza Strip.