As Gaza and Israel emerge from 11 days of conflict, mediators are seeking to cement the truce and prevent more violence in the longer term.
An Egyptian team was in Israel on Saturday, while the US Secretary of State Antony Blinken could visit the region next week.
Both Israel and the Palestinian militant group Hamas have claimed victory in the latest conflict.
More than 250 people were killed, most of them in Gaza.
The fighting began on 10 May after weeks of rising tension that culminated in clashes at al-Aqsa, a holy site revered by both Muslims and Jews, in occupied East Jerusalem. Hamas began firing rockets after warning Israel to withdraw from the site, triggering retaliatory air strikes.
Since the truce went into force on Friday, Israeli PM Benjamin Netanyahu has said the degrading of Hamas's military power by air bombardment was an "exceptional success".
He added: "If Hamas thinks we will tolerate a drizzle of rockets, it is wrong" and pledged a "new level of force" in response.
Meanwhile, Hamas has spoken of what it called the "euphoria of victory" and its leader Ismail Haniyeh said the conflict had "opened the door to new phases that will witness many victories".