Hamas rejected the proposal and said its forces would keep fighting as long as Israeli troops remained in Gaza. The Islamist group said it had fired at the Israeli cities of Tel Aviv and Ashdod. No damage or injuries were reported.
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 offensive.
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"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.
There appeared to be little progress on the diplomatic front and in international efforts to secure an end to the conflict.
U.S. Secretary of State John Kerry flew back to Washington overnight after meeting in Paris with foreign ministers of France, Italy, Britain, Germany, Turkey and Qatar.
At least 1,050 Gazans - mostly civilians - have been killed in 20 days of fighting. An Israeli soldier was also killed overnight by cross-border mortar fire, bringing the army death toll to 43 soldiers, with three civilians killed in Israel by rocket and mortar attack. The positions of both Israel and Hamas regarding a long-lasting halt to hostilities appear as far apart as ever.
Hamas wants an end to the blockade of Gaza before agreeing to halt hostilities. Israeli officials said any ceasefire must allow the military to carry on hunting down the Hamas tunnels.
Some of the tunnels reach into Israeli territory and have been used to carry out surprise attacks on Israelis. Other underground passages serve as weapons caches and Hamas bunkers.
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Israel says its forces have uncovered more than 30 tunnels, with four shafts discovered on Saturday alone. One official said troops had found it easier to operate during the truce as the immediate threat to their safety was diminished.
The Gaza turmoil has stoked tensions amongst Palestinians in mainly Arab East Jerusalem and the occupied West Bank.
Medics said eight Palestinians were killed on Friday in incidents near the West Bank cities of Nablus and Hebron - the sort of death toll reminiscent of previous uprisings against Israel's prolonged military rule there.
During the lull in fighting inside Gaza on Saturday, residents flooded into the streets to discover scenes of massive destruction in some areas, including Beit Hanoun in the north and Shejaia in the east.
Israel hopes that the images of widespread desolation will persuade Gazans to put pressure on Hamas to stop the fighting for fear of yet more devastation.