A ceasefire between Israel and the Islamist Hamas movement that runs the Gaza Strip appeared to be holding on Thursday.
Israel radio said some rockets had been fired from Gaza, but there was no sign of an Israeli response.
Overnight, thousands of Gaza residents poured on to the streets to celebrate, waving flags and setting off fireworks.
The UN Security Council has called on Israel and Hamas to uphold the agreement, brokered by Egypt.
Overnight, the Israeli Defence Forces (IDF) said it had arrested 55 "terror operatives" in the West Bank, including some at a senior level, in an effort to "restore calm".
There have been a number of protests in the West Bank in the past week against Israel's Pillar of Defence operation, with some protesters clashing with Israeli soldiers.
In its first statement since the current flare-up began, the Security Council also commended Egyptian President Mohammed Mursi and others involved in the diplomatic effort.
UN Secretary General Ban Ki-moon, who has been meeting regional leaders during the conflict, welcomed the ceasefire and said it was urgent that humanitarian aid be delivered to Gaza.
"We are all aware that there are many details that must be solidified for a broad, durable ceasefire to take firm hold over the longer term," he said.
"It is imperative that both sides stick to the ceasefire in order to allow these underlying issues to be addressed."
Five Israelis and more than 150 Palestinians have died since the outbreak of violence began last week.
The Israeli military said three rockets had been fired from Gaza since the ceasefire came into effect, two of which were shot down by the Iron Dome defence system. It said there had been no fire in either direction since midnight.
The BBC's Kevin Connolly in Jerusalem says that in the early stages of the ceasefire, success will be measured from minute to minute.
The more time that passes without rocket fire from Gaza or an air raid from Israel, the more confident civilians on both sides will feel, he adds.
Under the deal, Israel has agreed to end all hostilities and targeted killings, while all Palestinian factions will have to stop firing rockets into Israel and staging border attacks.
Israel must also begin talks about opening Gaza's border crossings and easing restrictions on the movement of people and goods.
The truce was announced in Cairo on Wednesday by Egyptian Foreign Minister Kamel Amr.
Alongside him was US Secretary of State Hillary Clinton who had taken part in the negotiations, first in Jerusalem and later in Cairo.
The announcement set off ecstatic celebrations in Gaza, where residents who had spent days sheltering from air strikes took to the streets.
The BBC's Jon Donnison in Gaza City says the city was transformed as people flooded into the streets, many of them firing weapons into the air.
But the truce is essentially a maintaining of the status quo, our correspondent adds, and it is hard to see either side sticking to it unless there are further talks and a broader peace plans.
Hamas's exiled political leader Khaled Meshaal said Israel's offensive had "failed" and that the deal met Hamas's main demands.
All the crossings into Gaza would re-open, including those with Egypt, Mr Meshaal said.
In Gaza itself, Hamas spokesman Ihab Hussein hailed the truce as a victory.
"These people made this victory by their patience, by the blood of our people," he said.
"They (the Israelis) will open the borders, they will stop assassinating and killing our people. We will live in calm and in a peace[ful] situation."
In Israel, however, small protests were held in communities such as the southern town of Kiryat Malachi, where three people were killed by a Gaza rocket during the conflict, army radio said.
Protesters said the military should have hit Hamas harder and some banners denounced "agreements with terrorists".
Despite the ceasefire, Israeli schools within 40km of the Gaza Strip were being kept closed on Thursday as a precaution, the military said.
Israel says it targeted 1,500 "terror sites" during Operation Pillar of Defence.
It says its targets included 30 senior militants, 980 underground rocket launchers and 140 smuggling tunnels.
The Israel Defense Forces (IDF) said that, for the first time, militants in Gaza had fired long-range rockets, such as the Fajr-5, toward Tel Aviv and Jerusalem.
A statement from the office of Israeli Prime Minister Benjamin Netanyahu said he had agreed to a US suggestion "to give a chance to Egypt's proposal for a ceasefire and so give an opportunity to stabilise the situation and calm it before there will be need to apply greater force".
Violence continued right up to the 21:00 (19:00 GMT) ceasefire deadline. During the day, a bomb exploded on a bus in the Israeli city of Tel Aviv, wounding several people. At least 13 people died in Gaza on Wednesday.
Israel launched its offensive, which it says was aimed at ending rocket fire from Gaza, with the killing of a Hamas military leader.