It has been agreed among resistance factions to endorse a 24-hour humanitarian calm, Hamas spokesman Sami Abu Zuhri told Reuters, saying the calm should start at 2.00 pm.
An Israeli official said the truce was being reviewed.
However, as 2.00 pm came and went, the sound of heavy Israeli shelling could be heard within Gaza and sirens sounded in Israeli communities near the border area, suggesting Palestinian militants had fired missiles at them.
Israel had called off its own 24-hour truce earlier in the day after Hamas launched rockets into southern and central Israel, and Palestinian medics said at least 10 people had died in the wave of subsequent strikes that swept Gaza.
Some 1,060 Palestinians, mainly civilians and including many children, have been killed in the 20-day conflict. Israel says 43 of its soldiers have died, along with three civilians killed by rocket and mortar fire out of the Mediterranean enclave.
Israel and the Hamas Islamists who control Gaza had agreed to a 12-hour ceasefire on Saturday to allow Palestinians to stock up on supplies and retrieve bodies from under the rubble.
Israeli Prime Minister Benjamin Netanyahus cabinet decided to extend the quiet until midnight on Sunday, on condition that its forces could continue to track down and destroy militant tunnels that criss-cross the Gaza border.
After initially rejecting the extension, Hamas spokesman Abu Zuhri said Hamas had accepted a UN truce request on Sunday in light of the upcoming Muslim holiday of Eid al-Fitr, which is expected to start in the next couple of days.
Netanyahu was due to convene his cabinet later on Sunday to decide how to move forward, and at least one senior minister said Israel must step up its
After what we saw this morning, it is clear we need to resume fighting with even greater force, communications minister Gilad Erdan told Army Radio.
Israel launched its Gaza offensive on July 8 to halt rocket attacks by Hamas and its allies, which have struggled under an Israeli-Egyptian economic blockade on Gaza and were angered by a crackdown on their supporters in the nearby occupied West Bank.
After aerial and naval bombardment failed to quell the outgunned guerrillas, Israel poured ground forces into the Gaza Strip 10 days later, looking to knock out Hamas's rocket stores and destroy the vast network of tunnels.
Diplomatic efforts led by US Secretary of State John Kerry to end the 20-day conflict have shown little sign of progress. Israel and Hamas have set conditions that appear irreconcilable.
Hamas wants an end to the Israeli-Egyptian blockade of Gaza before agreeing to halt hostilities. Israel has signaled it could make concessions toward that end, but only if Gazas militant groups are stripped of their weapons.
Hamas must be permanently stripped of its missiles and tunnels in a supervised manner, economy minister Naftali Bennett said, In return we will agree to a host of economic alleviations, the security cabinet member said on Facebook.
Kerry flew back to Washington overnight after meeting in Paris with foreign ministers of France, Italy, Britain, Germany, Turkey and Qatar, with no sign of progress.
The main UN agency in Gaza, UNRWA, said 167,269 displaced Palestinians have taken shelter in the organisations schools and buildings, following repeated calls by Israel for civilians to evacuate whole neighborhoods ahead of military operations.