Palestinian Authority President Mahmoud Abbas warned Monday that a cease-fire in Gaza remained fragile and he backed Egypt-led efforts to bring calm. Abbas met with French President Nicolas Sarkozy as part of his effort to drum up diplomatic support for a unity government of Palestinian factions and to push for a role in rebuilding Gaza, controlled by rival Hamas. Speaking to reporters after the meeting, Abbas called for a "solution with Hamas in the framework of a government of national unity," but rejected the group's call for a new Palestinian political structure. Abbas said the situation in Gaza "remains fragile" - with "military operations" and "Israeli bombardments" continuing that have strained the informal cease-fire. "We hope that all this is going to stop and that the efforts provided by Egypt are going to succeed in bringing back calm and allowing for a Palestinian reconciliation," he said. The visit to Paris to meet with Sarkozy - who helped broker the Gaza cease-fire - came at the start of a diplomatic push by Abbas around Europe aimed at finding sturdier solutions for Gaza. Earlier, Sarkozy met Qatar's prime minister, Sheik Hamad bin Jassem al-Thani, whose Persian Gulf country has emerged as a regional mediator since helping to resolve a political crisis in Lebanon last year. Al-Thani insisted Hamas should not be sidelined from peace efforts, and said Arab nations should not play favorites in pushing for a solution. "We must work for a government of national unity between the Palestinians," al-Thani told reporters. "Arab countries cannot support this or the other Palestinian party against another." "There should not be efforts to delete or distance one of the Palestinian parties present on the ground," he said, referring to Hamas. He also urged the international community to pressure Israel to permanently stop its bombardments. Also Monday, President Barack Obama's Mideast envoy, George Mitchell, met with Sarkozy's chief of staff before sitting down with French Foreign Minister Bernard Kouchner for lunch. Mitchell met with Abbas and other Palestinian officials last week. During their meeting, Kouchner and Mitchell discussed their common desire to see that the cease-fire in Gaza holds for the long term, said a French diplomatic official. Kouchner stressed the need for inter-Palestinian dialogue and for the border crossings into Gaza to be reopened, the official said on condition of anonymity because he was not authorized to speak publicly on the matter. Abbas' aides have said he is on a European tour - with stops at EU parliament in Strasbourg, as well as is Britain, Italy, Turkey and Poland - in hopes of gaining support for a Palestinian unity government that would likely have to involve Hamas but would also include independents as cabinet ministers. The Palestinian leader also wants international backing for his demands that he be given a role in Gaza reconstruction, and that his troops be deployed at the Gaza border crossings with Israel and Egypt. Hamas, for now, is cool to both ideas. The group on Monday sent a delegation to Egypt in hopes of wrapping up a long-term cease-fire. In Cairo on Sunday, Abbas told reporters he would not hold reconciliation talks with Hamas as long as it rejects his authority. The two sides have been divided since Hamas seized Gaza in 2007. Abbas' Fatah rules the West Bank. Kouchner last week suggested France was open to the idea of a unity government if Hamas softens its stance.