Hamas has demanded an end to Israeli and Egyptian blockades of the Gaza Strip and the opening of a seaport in the enclave - a project Israel says should be dealt with only in any future talks on a permanent peace deal with the Palestinians.
Egypt's Foreign Ministry urged "both sides to exploit this truce to resume indirect negotiations immediately and work towards a comprehensive and lasting ceasefire agreement".
Israeli Strategic Affairs Minister Yuval Steinitz said in a radio interview on Monday that disarming Gaza militants was crucial to sustain a long-term truce and he hoped this could be done by diplomacy rather than force.
"I certainly hope that there will be a diplomatic solution. If there will not be a diplomatic solution, I am convinced that sooner or later we will have to opt for a military solution of taking temporary control of Gaza to demilitarise it again," he told Israel Radio.
In Gaza, shops began to open and traffic was normal as displaced families returned to the homes they had been forced to abandon during Israeli attacks, expressing hopes that this truce would last after a series of failed ceasefires.
"God knows if it is permanent," said Abu Salama, a resident of Gaza's Shejaia district, as he and his family headed home on a donkey cart.
"A truce, no truce, it is becoming like Tom and Jerry. We want a solution," he said.
The new three-day ceasefire won praise from United Nations Secretary General Ban Ki-moon, who hoped it might lead to a durable ceasefire.
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Israeli air strikes and shelling on Sunday killed nine Palestinians in Gaza, medics said, in a third day of renewed fighting since the last truce ended.
One air strike destroyed the home of Gaza City's mayor, Nezar Hijazi, across the street from the Reuters bureau where reporters and cameramen took cover as the explosion occurred. There were no casualties in the attack because Israel telephoned warnings to residents in the house and neighbouring buildings.