Hamas said it had endorsed a call by the United Nations for a pause in the fighting in light of the upcoming Muslim holiday of Eid al-Fitr, which starts in the next couple of days.
Some firing had continued after the time that Hamas had announced it would put its guns down and Israeli prime minister Benjamin Netanyahu questioned the validity of the truce.
"Hamas doesn't even accept its own ceasefire, it's continuing to fire at us as we speak," he said, adding that Israel would "take whatever action is necessary to protect our people".
Nonetheless, Gaza Strip residents said Israeli shelling and Hamas missile launches had slowly eases through the afternoon, suggesting a de-facto truce might be taking shape as international efforts to broker a permanent ceasefire appeared to flounder.
However, Israel's military has said it will need more time to destroy a warren of tunnels beneath the Gaza border.
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.
Netanyahu's cabinet voted to extend the truce until midnight last night at the request of the UN, but called it off when Gaza militants launched rockets into Israel in the morning.
Palestinian medics said at least 10 people had died in the wave of subsequent strikes on Gaza.
Some 1060 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 enclave.
Israel launched its Gaza offensive on July 8, saying its aim was to halt rocket attacks from the enclave.
After aerial and naval bombardment failed to quell outgunned militants, Israel poured ground forces into the Strip 10 days later, to destroy rocket stores and the network of tunnels.
The army says its drive to find and eliminate tunnels would continue through any temporary truce.
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 economic blockade of Gaza before agreeing to halt hostilities. Israel has signalled it could make concessions to that end, but only if Gaza's 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.
Mr Kerry flew back to Washington overnight after spending most of the week in Egypt trying to bridge the divide, putting forward some written proposals to Israel on Friday.
Speaking off the record, cabinet ministers described his plan as "a disaster", saying it met all Hamas's demands, such as lifting the Israeli-Egyptian blockade completely and ignored Israeli terms, such as stripping Hamas of its rockets.