And two senior Hamas officials said the Palestinian militant movement would not extend a 72-hour ceasefire in Gaza that expires at 0500 GMT on Friday, accusing Israel of rejecting their demands for a truce.
A leader of the Palestinian Islamic Jihad, a smaller faction in Gaza that is also present in Cairo-mediated truce talks, confirmed the factions had decided not to extend the ceasefire. A short while prior to that, the Israeli army sent out a text message to journalists, saying: "Just now, two rockets fired from Gaza hit southern Israel. No injuries reported".
There was no immediate Israeli military response, an army spokeswoman told AFP.
Hamas spokesman Sami Abu Zuhri however said that "the Israeli claim of firing two rockets from Gaza is only an accusation to confuse the issues". Israel had said earlier it was ready to "indefinitely" extend the ceasefire.
Following the Hamas indication it would refuse to extend the truce, an Israeli official warned that "we might have to continue" the military campaign.
"The reaction must be harsh" if Hamas renews its fire at Israel, head of the influential parliamentary foreign affairs and defence committee Zeev Elkin told public radio, without going into detail.
Hamas representatives and those of the Palestine Liberation Organisation (PLO) and Israel had been meeting in Cairo for talks with Egyptian mediators on extending the ceasefire.
A senior Palestinian official earlier accused Israel of procrastinating, warning it could lead to a resumption of the fighting when the deadline runs out. "The Israeli delegation is proposing extending the ceasefire while refusing a number of the Palestinian demands," he said, without elaborating.
A spokesman for Hamas's armed wing, the Ezzedine al-Qassam Brigades, warned late Thursday that fighting would resume if their demands were not met, first and foremost to open a sea port to the blockaded Palestinian enclave.
"If there is an agreement, it will be possible to extend the truce, but if there is not, we will ask the delegation to withdraw from the talks," a spokesman using the nom-de-guerre Abu Obeida said in a televised address.
Four weeks of bloodshed between Israel and Hamas killed 1,890 Palestinians, and 67 people on the Israeli side, almost all soldiers.
Ayman Taha, a former spokesman for Hamas -- the son of one of the group's founders -- was found dead Thursday in a neighbourhood of the city that was heavily bombed by Israel, the movement said.
UN figures indicate that 73% of the Palestinian victims -- or 1,354 people -- were civilians. Of that number, at least 429 were children.
Hamas and Palestine Liberation Organisation (PLO) officials laid out a number of demands, starting with the lifting of Israel's eight-year blockade on Gaza. They also want the release of around 125 key prisoners held in Israeli jails.
Israel ready to resume operations
Despite the withdrawal of all its troops from Gaza by the time the three-day truce began early on Tuesday, Israel has retained forces along the border who are ready to respond to any resumption of fighting.
Speaking in Jerusalem after a visit to Gaza, International Committee of the Red Cross president Peter Maurer said he was "deeply distressed and shocked" at the impact of violence, saying the scale of the civilian losses must not happen again.
And he suggested there may have been violations of international humanitarian law.
Israeli Prime Minister Benjamin Netanyahu stressed to Maurer that "every one of these civilian deaths is a tragedy" while blaming Hamas of "both targeting civilians and hiding behind civilians". Netanyahu also asked Maurer to help retrieve the bodies of two Israeli soldiers missing in Gaza after being killed in fighting there.
In some areas, there are scenes of utter devastation, with certain districts reduced to a sea of rubble and shattered hulks of buildings, an AFP correspondent said.
British aid agencies launched an emergency appeal for Gaza, with the Disasters Emergency Committee (DEC), which brings together 13 leading British charities at times of crisis, said half a million people had been forced from their homes, and that up to 1.5 million had limited access to water, sanitation or medical care.
US President Barack Obama upped the pressure on the talks by saying Gaza could not remain forever cut off by Israel's blockade which has been in place since 2006. "Long-term, there has to be a recognition that Gaza cannot sustain itself permanently closed off from the world," he said, adding the Palestinians needed to see "some prospects for an opening of Gaza so that they do not feel walled off".
And London, Paris and Berlin submitted an initiative offering an outline for rebuilding Gaza while ensuring Israel's security concerns are properly addressed, a diplomatic source said.
The proposal aims to strengthen the hand of Palestinian president Mahmud Abbas and his Palestinian Authority while clamping down on Gaza-based militant groups.
It also envisages opening the Rafah border crossing with Egypt, then eventually opening other crossings to Israel. It also refers to the opening of a commercial port in Gaza, the source said.