Palestinians are warning of renewed violence if Hamas and Israeli officials cannot agree to a deal before Tuesday's midnight truce deadline.
The two sides are holding intense, indirect talks in Cairo after agreeing Monday to a 24-hour cease-fire extension, the third such truce in 10 days.
The chief Palestinian negotiator, Azzam al-Ahmad, said Tuesday the "cycle of violence" will continue in the Gaza Strip if the talks do not succeed.
"We agreed to the cease-fire for just one day, just one day. Tomorrow we will agree or we will not agree. We hope to use every minute of the next 24 hours to reach an agreement, or else the cycle of violence will continue,” said Ahmad.
The announcement of the extension Monday came just minutes before the cease-fire was set to expire at midnight local time.
There was no indication that negotiators are close to reaching a deal to stop more than a month of fighting between Israel and Hamas, which runs the coastal enclave along the Mediterranean.
Israeli Prime Minister Benjamin Netanyahu on Monday warned the Israeli army is ready to respond with force if Hamas resumes firing rockets at Israel, as it did when the first cease-fire was about to expire more than a week ago.
“Together, we are conducting this complicated campaign with determination and responsibility. We are ready for any scenario. The Israeli team in Cairo has been instructed to insist on Israel's security needs and the IDF is prepared for very strong action if fire is resumed," said Netanyahu.
Egyptian mediators have been conducting indirect negotiations, carrying truce proposals back and forth between the Israelis and the Palestinians. Israel has refused direct talks because the Palestinian delegation includes Hamas, which it considers a terrorist group.
The gap between Israel and the Palestinians remains wide, with Israel demanding the disarming of Hamas and an end to its cross-border rocket attacks. The Palestinians are calling for the end of Israel's eight-year blockade of impoverished Gaza.
The five weeks of fighting have left more than 2,000 people dead, most of them Palestinians. It also has left Gaza neighborhoods in rubble from Israeli airstrikes. Sixty-seven Israelis have also been killed. All but three were soldiers.
Norway says once a lasting truce is reached, it will host a conference with Egypt to look for international donors to rebuild Gaza.