Both sides have agreed to a 12-hour "humanitarian" ceasefire in Gaza that started at 1030 IST today, putting a brief stop to a conflict that has killed more than 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 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," said Fabius, who went on to brief Palestinian President Mahmud Abbas on the phone.
Kerry and Fabius met with their counterparts from Britain, Germany, Italy, Qatar and Turkey, as well as a representative from the European Union.
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"The massacres are unbearable, they cannot continue," said a top French diplomat who refused to be named.
Kerry, who has been leading international efforts to reach a ceasefire, 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.
But both Israel and Hamas remain at odds over the shape of a final deal.
The Jewish state, meanwhile, is adamant that it wants to destroy an apparently sophisticated network of tunnels through which Hamas militants can infiltrate from Gaza to wage attacks.