Gaza: Uneasy calm after UN ceasefire call
Sporadic attacks by both Israel and Palestinian militants have punctuated a lull in fighting after the quietest night in the 21-day conflict.
There were no Israeli air strikes overnight though they resumed in the morning after a rocket hit the southern Israeli city of Ashkelon.
Earlier the UN Security Council urged a halt to hostilities to coincide with the Muslim holiday of Eid al-Fitr.
Israel launched its offensive three weeks ago after a surge in rocket fire.
More than 1,030 Palestinians, mostly civilians, and 43 Israeli soldiers and two Israeli civilians have been killed. A Thai national in Israel has also died.
The Security Council called on Sunday night for an "immediate and unconditional humanitarian ceasefire" in Gaza over and beyond the holiday period.
Both the Palestinian and Israeli envoys to the UN criticised the statement, for different reasons.
On Monday, UN Secretary General Ban Ki-moon on Monday urged both Israel and Hamas to build on the lull in fighting.
"As people around the world mark Eid al-Fitr, the end of the holy month of Ramadan and a time for overcoming differences, the secretary general calls on parties to build on the current calm," Mr Ban's spokesman said.
He added that Mr Ban "calls on the parties to renew a humanitarian pause in Gaza and reiterates his demand for a durable ceasefire that could set the ground for the start of comprehensive negotiations".
At the scene: Martin Patience, BBC News, Gaza
I think the big hope here is that the patchwork of ceasefires we have seen in the past couple of days will become more sustainable and durable, that through international pressure we will see the ceasefires hold and hostilities end.
This was perhaps the quietest night in the Gaza Strip that we've seen in the three weeks since this operation began. Today marks the start of Eid al-Fitr, the end of Ramadan, and it is a festival which is supposed to last three days, so people here will certainly welcome the quiet.
But the reality is that there is not a great deal to celebrate in Gaza. More than 1,000 Palestinians have been killed in the fighting, most of them civilians. More than 100,000 Palestinians have been displaced from their homes. So people will welcome this respite but there is still uncertainty.'Night of prayers'
Israel's military launched three air strikes on rocket sites after the rocket attack on Ashkelon.
A boy aged four was killed in one of the strikes, Gaza's health ministry said.
Rockets were also fired at the Sdot Negev and Eshkol districts of Israel, Israel's Haaretz newspaper reports.
An Israeli soldier was wounded in northern Gaza where the military wing of Hamas, the Izzedine al-Qassam Brigades, said it had "clashed" with Israeli infantry.
Gazans have been praying and visiting the graves of relatives and friends killed during the 21-day conflict.
"Eid here is limited to religious activities, some of the displaced people have returned to inspect their destroyed homes," the BBC's Rushdi Abualouf in Gaza said in a tweet. On a normal Eid, he added, "Palestinians visit their relatives, kids play in the streets".
Traffic on Gaza's roads and foot traffic in its markets was sparse, Haaretz reports. "Those that weren't hit and still left their homes only looked for basic needs, perhaps for their children, all we did tonight was pray for a lull in the fighting and pray for better days," a Gaza resident told the paper.
"The situation now is an unlimited truce," Israel's chief military spokesman, Brig Gen Motti Almoz, told Israel Radio. "The IDF [Israeli Defence Forces] is free to attack after any fire if there is any."
The UN Security Council called for a "durable" truce based on an Egyptian initiative, under which a pause in hostilities would lead to substantive talks on the future of Gaza, including the opening of Gaza's border crossings.
The Palestinian representative at the UN, Riyad Mansour, said the statement did not go far enough and that a formal resolution was needed demanding that Israel withdraw its forces from Gaza.
Israel's ambassador Ron Prosor accused the Security Council statement of bias for not mentioning Hamas and the firing of rockets at Israel.
Opinion polls published at the weekend suggest there is still widespread support among Israelis for the military operation.
At the scene: Bethany Bell, BBC News, Jerusalem
While Israel's Prime Minister Benjamin Netanyahu is facing increasing international pressure for a long-term ceasefire with Hamas, at home there is strong public support for the army's offensive in Gaza. A poll published by Israel's Channel 10 television on Sunday suggested 87% of Israelis were in favour of continuing the Gaza operation - and just 7% wanted a full ceasefire.
There are concerns about the rising number of casualties among Israeli soldiers but people here want the rocket fire on Israel to stop. The sound of sirens over central and southern Israel has become part of everyday life. And many are very concerned about the new threat posed by the network of cross-border tunnels from Gaza.
At her home on a kibbutz close to the Gaza border, one woman said she was afraid. Rockets can be intercepted by Iron Dome, she told me, referring to Israel's missile defence system. "But there's no Iron Dome protection against Hamas fighters coming up through the tunnels to kidnap and kill us," she added.Pressure on Obama
US President Barack Obama called for an immediate, unconditional humanitarian ceasefire in a phone call to Israeli Prime Minister Benjamin Netanyahu on Sunday.
A long-term solution, he added, would have to allow "Palestinians in Gaza to lead normal lives" and "must ensure the disarmament of terrorist groups and the demilitarisation of Gaza".
Israel launched its military offensive on 8 July with the declared objective of stopping Hamas, the Islamist group which controls Gaza, firing rockets from Gaza into Israel.
On 18 July, it extended operations with a ground offensive, saying it was necessary to destroy tunnels dug by militants to infiltrate Israel.
Are you in Israel or Gaza? How are you affected by the situation? Email your experiences to email@example.com using the subject 'Israel Gaza'.