Renewed talks aimed at achieving a truce between Israel and Hamas militants in Gaza are expected as the conflict enters its seventh day.
Overnight, explosions were heard in Gaza and sirens sounded in southern Israel, although correspondents said it had been "relatively quiet".
Israeli leaders met late into the night to discuss Egyptian proposals to end the violence.
Further talks are expected to take place in Cairo on Tuesday.
Meanwhile, the UN Security Council is debating a statement calling on both parties to stop attacks and address humanitarian needs in Gaza.
More than 100 people have died in the Gaza Strip since the Israel bombardment began and at least three Israelis have been killed by rockets fired by Palestinian militants.
On Monday, a commander of the Islamic Jihad militant group died in an air strike on a Gaza City tower block housing media organisations. A couple and their two small children were also killed in northern Gaza.
The Israeli army said 67 rockets fired from Gaza landed in Israel during the day.
Israeli troops are massed along the border, raising fears of a ground offensive similar to that of 2008-09.
However, Israeli officials are quoted as saying that any possible ground invasion of Gaza has been put on hold while the ceasefire talks continue.
Overnight, air-raid sirens sounded in parts of southern Israel including Ashkelon, Kiryat Gat and Sderot. Some rocket and mortar fire was heard although no casualties were reported, Israel Radio said.
The BBC's Paul Danahar in central Gaza tweeted that it had been a quieter night, with no naval bombardment and relatively few air strikes.
It is perhaps the first real indication of political progress in Cairo, he added.
Egypt has been trying to broker a ceasefire with the help of Qatar and Turkey.
As international momentum to stop the conflict gathered pace, UN Secretary General Ban Ki-moon was to meet Arab league Chief Nabil al-Arabi in Cairo on Tuesday morning. He is then due to travel on to Israel.
Turkish Foreign Minister Ahmet Davutoglu and Arab foreign ministers are expected to visit Gaza on Tuesday.
Israel's nine most senior ministers ended their talks in the early hours but there was no word on their reaction to the latest Egyptian proposals.
The content of the Egyptian plan is not known, but both Israel and Hamas have presented conditions.
Israel's include no hostile fire of any kind from Gaza and international efforts to prevent Hamas from rearming, while Hamas is demanding an end to the blockade on Gaza and "Israel's assassinations".
The Israeli newspaper Haaretz said that Tuesday's talks in Cairo were expected to be "decisive".
It said Israeli delegates planned to return there on Tuesday to present Israel's response.
Meanwhile, UN Security Council members have been debating a draft statement on Gaza and are awaiting a response from their governments.
The statement, proposed by Arab ambassadors, calls on both parties to stop all military activities and address the humanitarian needs in Gaza.
The BBC's Barbara Plett at the UN says Western diplomats have been pushing for references to Hamas rocket fire and Israel's right to self-defence, rather than just a general call to halt the violence.
They say they are leaving it to their governments to make the final decision.
Russia, however, has said that if the council cannot agree it will table a resolution to be put to the vote on Tuesday.
This seems to be a tactic to put pressure on the US, our correspondent says, by forcing them to veto a resolution if they don't agree to the statement.
Palestinian UN envoy Riyad Mansour said the Security Council should not "remain on the margin".
He said it was important for the "the Security Council to shoulder its responsibility and stop this aggression against our people".
On Monday, US President Obama spoke to his Egyptian counterpart Mohamed Mursi and to Israeli President Benjamin Netanyahu, discussing ways to de-escalate the situation, the White House said.
Khaled Meshaal, political leader of the Islamist movement Hamas which controls Gaza, said that a truce was possible in Gaza - as was further escalation of the conflict.
Hamas seized control of Gaza in 2007, a year after winning a decisive victory in general elections. Israel withdrew from the strip in 2005 but maintains a blockade around it.
Israel, as well as the United States and the European Union, regards Hamas as a terrorist organisation.