The remarks came on the eve of a key meeting of the executive committee of the Palestine Liberation Organization (PLO) to discuss forming a new cabinet after the government collapsed this week amid a deepening rift with Hamas, the de facto rulers of the Gaza Strip.
Abbas is thought to be seeking to replace the government of technocrats - formed last year to overcome rivalry between Palestinian factions - with a government of politicians.
"(Abbas) told me this government of national unity could only include women and men who recognize Israel, renounce violence and who are in agreement with the principles of the (Mideast) Quartet," Fabius said at a press conference in Jerusalem after holding talks with Abbas in Ramallah.
Noting that those conditions ruled out Hamas, Fabius added: "And that suits us perfectly."
The Islamist Hamas group has been designated a terrorist organization by the European Union and the United States.
The Palestinian unity agreement signed in April 2014 had sought to end seven years of bad blood between Abbas's Fatah movement and Hamas.
Abbas's move to dissolve the government came at a critical time, with Hamas sources saying it is holding separate, indirect talks with Israel on ways to firm up an informal ceasefire that last August ended a 50-day war in Gaza.
It was not immediately clear whether the government's collapse on Wednesday was directly linked to the talks.
Fabius said he had asked Prime Minister Benjamin Netanyahu about the contacts with Hamas. "If I understood his response, it means that somehow, I don't know how, there are conversations about Gaza and about improving the humanitarian situation" in the blockaded territory, Fabius said.
Sunday's meetings in Ramallah and Jerusalem were part of efforts by Fabius aimed at reviving Israeli-Palestinian peace talks that have been comatose since a major US push for a final deal ended in failure last year.