"We want a long-term arrangement," Lieberman said.
His remarks came on the fifth day of strikes on Gaza which left 55 people dead, while militants from the Strip fired hundreds of rockets at the Jewish state, one of which killed three.
Earlier on Sunday, Prime Minister Benjamin Netanyahu said Israel was ready to "significantly expand" its operation against militants in the Hamas-run Gaza Strip even as he prepared to receive Fabius, who is on a whirlwind truce mission to the region to promote a truce.
Speaking alongside Lieberman, Fabius said the current situation was "an emergency situation.
"War must be avoided, and can be avoided," he said.
"The solution is a ceasefire. We want to help to find the terms of a ceasefire," Fabius said.