More than 18 hours later, the nascent truce appeared to be holding, although Israeli police said eight rockets and mortar shells were fired without causing injury or damage.
One rocket fired late on Tuesday landed in a parking lot in the city of Netivot, lightly wounding one person and damaging some vehicles, according to the police.
The skies over Gaza remained calm.
The United States welcomed the truce.
"There are reports that the Egyptians have been able to negotiate some calm. If, in fact, that's the case, that would, of course, be very welcome," State Department spokeswoman Victoria Nuland said in Washington.
Home Front Defence Minister Matan Vilnai confirmed Israel had reached an unwritten "understanding" with militant groups in Gaza.
"Apparently things are calming down and this round of confrontations appears to be behind us," he told public radio.
Defence Minister Ehud Barak echoed him: "This morning the situation is relatively quiet," he told reporters.
In Gaza, an Islamic Jihad spokesman said the radical group was willing to respect the deal, but Israel must end its targeted killings of militants.
"We accept a ceasefire if Israel agrees to apply it by ending its aggressions and assassinations," Daud Shihab told AFP.
Both parties warned, however, that the agreement would be short lived if the other side stepped out of line.
"Our message is clear," Prime Minister Benjamin Netanyahu told a conference of senior civil servants in Jerusalem. "Calm will bring calm. Anyone who disturbs it, or even tries to disturb it, will be in our gunsights."
"Any Israeli violation requires a strong response by all factions," said Fawzi Barhum, a spokesman for Gaza's Hamas rulers, who have been seeking Cairo's help to restore calm.
The truce, he said, "was not meant to tie the hands of the resistance and its right to respond forcefully to the killings and attacks."
News of the agreement emerged early on Tuesday after Cairo brokered what an Egyptian intelligence official described as a "comprehensive and mutual" truce.
"An agreement on ending the current operations between the two sides, including a halt to assassinations, came into force at 1:00 am," he told AFP, saying the deal resulted from "intensive contacts" with both sides.
But Vilnai denied Israel had agreed to halt the assassinations.
"Anyone involved in terrorism against Israel needs to know that they are in our sights," he warned.
Senior Israeli defence ministry official Amos Gilad said the deal had been concluded with Egypt, without direct contact with Gaza's Hamas rulers.
"We have agreed to quietness on condition there will be quietness."
Egypt has been involved in brokering numerous truce agreements between Israel and Gaza militant groups, but a Hamas MP on Monday accused Cairo of using Gaza's ongoing fuel crisis to put pressure on the Islamist movement to enforce a ceasefire.
"Egyptian intelligence officials offered to provide the government with the fuel needed to operate the power plant, to resume transportation and the operation of factories, in exchange for a truce on the ground in Gaza," Yunes al-Astal said in a statement sent to AFP.
Gaza's sole power plant shut down three times in the past two months due to fuel shortages, although Egypt has agreed to provide enough fuel to allow it to operate.
The violence kicked off on Friday with Israel's assassination of the head of the radical Popular Resistance Committees (PRC).
The strike prompted militants to fire hundreds of rockets and mortar rounds into southern Israel, wounding people and prompting the closure of schools within firing range of Gaza.
Israel responded with dozens of air strikes, targeting militants and weapons facilities.
Palestinian medics put the total death toll late on Monday at 25, with more than 80 injured.
Of those killed, 19 were militants -- 14 from Islamic Jihad, and five from the PRC -- and six were civilians, among them two minors.