At a joint news conference with his Jordanian counterpart, Nasser Judeh, Fabius said his regional tour seeks to help "break the spiral of violence and to protect the civilian population as much as possible" in Gaza, where the Israeli bombardment has killed more than 330 Palestinians.
"The human toll is already heavy… and I repeat here in Amman, our absolute priority must be the ceasefire," he told reporters.
"The Egyptian initiative remains on the table and the objective is ceasefire. Jordan, France and other countries support the initiative."
The truce plan, which Egypt had proposed take effect last Tuesday, calls for a ceasefire followed by indirect negotiations between Israel and Hamas.
But Hamas rejected the plan, insisting on negotiating key demands such as a guarantee to lift the blockade on Gaza's border crossings before it halts its rocket fire.
"This initiative has been widely supported by the international community and Arab countries," Fabius said.
"So now we need to ensure that the party that has rejected it accepts the plan to avoid losing more human lives," he added, describing the toll in Gaza as "extremely tragic".
Fabius arrived in Amman from Cairo, where here made an "urgent" call for the truce, following talks with Egyptian President Abdel Fattah al-Sisi, who is rallying international support for Cairo's ceasefire proposal while isolating Hamas.
The foreign minister said he would meet Israeli Prime Minister Benjamin Netanyahu night, following the stopover in Amman.
"All countries involved in efforts to stop the bloodshed in Gaza support the ceasefire initiative, which seeks to end the violence and protect civilians," said Judeh, whose country has a 1994 peace treaty with Israel.
Judeh condemned Israel's "brutal and barbaric aggression on Gaza as well as the targeting of civilians that led to the death or more martyrs", state-run Petra news agency quoted him as telling Italian Foreign Minister Federica Mogherini at a meeting.