Israel and Hamas agreed to a 12-hour humanitarian truce which the Jewish state later extended by four hours till midnight local time.
But shortly after the original truce expired at 1700 GMT, the Israeli military reported three mortar rounds fired from Gaza.
Hamas said it fired several rockets at Israel from the Gaza Strip, after the initial 12-hour truce ended. It said there was "no agreement" on an extension.
During the original 12-hour ceasefire, Palestinians, frantically scoured through rubble with medics saying over 130 bodies had been retrieved across the Gaza Strip.
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The discovery of the bodies under mounds of rubble had pushed the Palestinian death toll to over 1,000 in the coastal enclave since the conflict began on July 8.
About 5,870 Palestinians have been wounded in the 19 days of fighting, Gaza health officials say.
Three Israeli soldiers were killed in fighting in the Gaza Strip in the early hours of today before the humanitarian truce began, the army said.
Israel said it would continue to "locate and neutralise" Hamas tunnels during the pause. So far 31 tunnels have been discovered, with about half destroyed.
Before the truce began at 0800 local time, Israeli strikes killed at least 19 Palestinians overnight at a family home near Khan Younis in the southern Gaza Strip. Images showed relatives weeping as the bodies of five children were taken to a local morgue.
The Iron Dome defence system intercepted three rockets fired towards the southern Israeli town of Ashkelon overnight.
"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," said Fabius.
US Secretary of State John Kerry and Fabius met with their counterparts from Britain, Germany, Italy, Qatar and Turkey, as well as a representative from the European Union.