The US and UN have condemned the resumption of attacks between Gaza and Israel on Friday, urging both sides to cease hostilities.
Israel renewed strikes on Gaza soon after a three-day truce expired, saying it was in response to rocket fire by Hamas, which controls Gaza.
White House spokesman Josh Earnest said the parties should work towards a "sustainable ceasefire".
The UN said more suffering for civilians was "intolerable".
Hamas says it rejected an extension to the truce because Israel had failed to meet its demands.
More than 1,900 Palestinians, mostly civilians, have been killed in four weeks of violence in the Gaza Strip, the UN says.
Sixty-seven people have died on the Israeli side, including three civilians.
Israeli media reported more siren warnings on Saturday morning, signalling fresh rocket attacks.
Egypt, which is mediating between Israel and the Palestinians, has called for both sides to return to the negotiating table.
"Hamas' decision to resume rocket fire will not only put the people of Israel and of Gaza at greater risk, it will do nothing to meet the expectations of the Palestinian people," Mr Earnest said.
The US, he continued, hoped both parties would agree "to an extension of the ceasefire in the coming hours and ultimately conclude an agreement to cement a sustainable ceasefire".
UN Secretary General Ban Ki-moon also condemned the resumption of violence in the region.
He said in a statement: "More suffering and deaths of civilians caught up in this conflict is intolerable.
"The Secretary-General urges the parties to swiftly find a way back to respect of the humanitarian ceasefire and to continue negotiations in Cairo to reach a durable ceasefire."
A Palestinian delegation met Egyptian mediators in Cairo late on Friday. However, Israeli officials, who have pulled out of talks, said they would not "negotiate under fire" referring to the resumption of rocket attacks.
Senior Palestinian official Mustafa Barghouti told the BBC on Friday that rocket fire into Israel had come from other Palestinian factions, and not from Hamas.
Both sides suffered casualties on Friday.
A 10-year-old boy was among those killed, when an Israeli missile struck near a mosque in central Gaza, Palestinian officials said. A member of Islamic Jihad was also killed in Rafah, they added.
The Israel Defense Forces (IDF) said it had resumed its offensive with aircraft, tanks and gunboats on some "70 terror sites in response to continuing rocket fire".
Israel said militants began firing missiles from Gaza shortly before the ceasefire ended at 08:00 local time (05:00 GMT).
By Friday evening, the IDF said more than 40 rockets had been fired from Gaza into Israel since the truce expired.
When Hamas fires rockets, some Israelis have only 15 seconds to reach a bomb shelter. That’s not nearly enough time. http://t.co/gK4vSuk3Li— IDF (@IDFSpokesperson) August 9, 2014
The major sticking point in negotiations, Hamas says, is Israel's refusal to meet its demand of lifting the blockade on Gaza and the freeing of about 100 prisoners released in exchange for Israeli soldier Gilad Shalit in 2011 who have been rearrested.
The group also rejected Israel's call for the demilitarisation of Gaza.
However, Hamas said the Palestinian factions were willing to continue the talks despite the fresh violence.