Fabius was to meet Israeli President Shimon Peres, Prime Minister Benjamin Netanyahu, Defense Minister Ehud Barak and Foreign Minister Avigdor Lieberman, before travelling to
the West Bank to speak to Palestinian President Mahmoud Abbas.
He was not scheduled to visit Gaza.
Fabius intended "to call on all the parties to stop the escalation and offer France's help to reach an immediate ceasefire," his ministry said.
An anonymous official in Gaza told AFP that "serious discussions" on a truce were taking place on Sunday after Egyptian President Mohamed Morsi's statement on Saturday that there were "signs of the possibility of a ceasefire soon".
Fresh Israeli air strikes killed an 18-year-old child in Gaza on Sunday morning and two three-year-olds overnight, according to medical sources on the strip.
Since Israel’s latest offensive started 49 Palestinians, nine of them children, and three Israelis have been killed and 450 Palestinians and 18 Israelis have been wounded, according to the AFP wire service.
Eight rockets were fired from Gaza into Israel on Sunday morning. They caused no injuries or damage.
Up to 5,000 people demonstrated against the Israeli offensive in Paris on Saturday.
One of the organisers, Tawfiq Tahni of the France-Palestine campaign, called on President François Hollande “not to put the aggressor and the aggressed on the same footing” and to support the Palestinians’ bid for non-member state status at the UN.