A fresh three-day ceasefire agreed between Israel and Palestinian faction Hamas in Gaza was holding on Monday.
The agreement, which began at midnight (21:00 GMT Sunday), came after days of intense mediation by Egypt.
If the truce continues to hold, Israel will send negotiators to Cairo on Monday for talks on a longer-term deal.
Truce must lead to the lifting by Israel of its blockade of the Gaza Strip, Hamas Chief Khaled Meshaal tells AFP http://t.co/EYTWODAnWc— Agence France-Presse (@AFP) August 11, 2014
About 2,000 people have died in the conflict, which began on 8 July when Israel launched an operation intended to deter militant attacks from Gaza.
Those killed include more than 1,900 Palestinians, mostly civilians, according to the UN. Sixty-seven people have died on the Israeli side, including three civilians.
Israeli air strikes also continued throughout Sunday evening.
The Ynet website said the Israel Defense Forces had killed a militant in a tunnel in north Gaza before the ceasefire started.
While we were sending humanitarian aid into Gaza today, rockets struck the border crossing, forcing it to close. http://t.co/R362By58eV— IDF (@IDFSpokesperson) August 10, 2014
It is the second such ceasefire to be announced over the course of the conflict - the last one ended on Friday.
Since then, Israeli air strikes have killed at least 20 Palestinians and two Israelis have been injured by mortars.
After a weekend of tense talks that both sides had threatened to abandon, the surprise announcement of the truce came late on Sunday.
In a statement, Egypt's foreign ministry urged both sides to resume indirect negotiations and "work towards a comprehensive and lasting ceasefire agreement".
UN Secretary-General Ban Ki-moon also said he hoped it would give the two sides "another chance to agree on a durable ceasefire for the benefit of all civilian populations and as a starting point to address the underlying grievances on both sides."
Israeli Prime Minister Benjamin Netanyahu warned on Sunday that the military operation would not stop until there was a prolonged quiet.
"Israel will not engage in negotiations under fire," he told a cabinet meeting.
An unnamed Israeli official quoted by the Jerusalem Post said Israel was going into this truce with its eyes "wide open".
The official said Hamas was not only under military pressure from Israel but also under pressure from many in the Arab world, as well as people in Gaza, who want to see the crisis end.
Correspondents say Israel is likely to continue to push for Gaza to be demilitarised, and Hamas will continue to demand the blockade of Gaza to be lifted.
The issues have caused previous talks to founder.
The BBC's Wyre Davies in Jerusalem says the ceasefire should allow more humanitarian aid into Gaza, where thousands have been left homeless.
On the Israeli side, where dozens of communities have been evacuated, residents will also be able to return home.