Indirect talks between Israeli and Palestinian negotiators began in Cairo on Monday to find a long-term solution to the conflict in Gaza that has killed over 2,000 people as an Egyptian-brokered 72-hour ceasefire took hold in the Hamas-ruled territory.
The indirect talks are being mediated by Egypt and began a day after the two sides agreed to a new 72-hour cease-fire.
The Israeli military said that no rocket fire had been reported since the truce came into effect just after midnight.
After tense talks that both sides had threatened to abandon, the surprise truce announcement came late Sunday.
Militants in Gaza said they had fired several rockets towards Israel shortly before the truce got under way and Israeli air strikes had continued on Sunday evening, but the ceasefire has been respected since.
Israeli government spokesman Mark Regev said the Israeli military would be "ready to act to protect our people" if Hamas violated the agreement.
A previous cease-fire ended on Friday when militant groups in Gaza resumed rocket attacks on Israel, provoking renewed airstrikes from the Israeli military.
Four weeks of violence has killed 1,939 Palestinians and 67 on the Israeli side since Operation Protective Edge began on July 8.
The lull in fighting will help humanitarian aid reach some of the victims of the Gaza conflict.
A high-ranking Israeli delegation is in Cairo for talks with Palestinian factions. The delegation had quit the talks after Gaza armed groups resumed their rocket fire at Israel immediately upon the expiry of an earlier 72-hour truce on Friday.
However, the outcome of talks in Egypt remains uncertain, as both sides continue to refuse to budge from their demands.
Israel wants Hamas, the militant Islamic group that runs Gaza, to disarm as part of a demilitarisation of the territory.
Hamas, meanwhile, is demanding a series of measures, including an end to Israel's blockade on Gaza, an extension of fishing rights off the coast and the reopening of air and seaports.
Israeli authorities restrict the movement of goods and people in and out of Gaza, saying they need to prevent weapons being imported.
The latest outbreak of violence in the region erupted when Israel launched an offensive that it said was aimed at stopping rockets being fired from Gaza and at destroying a network of tunnels used by Palestinian militants for cross-border attacks.
Coverage: The war in Gaza