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The two leaders discussed the latest developments in the Palestinian territories and the Arab world, particularly following Israeli Prime Minister Benjamin Netanyahu's speech, SANA said.
The two presidents affirmed the need of uniting Arab stances to confront the Israeli settlement policy in the occupied Palestinian lands and obstacles placed to hinder the establishment of a sovereign Palestinian state.
Abbas expressed appreciation of the Syrian stance that supports finding a permanent solution to the Palestinian cause, SANA said.
They also discussed the inter-Palestinian reconciliation efforts, highlighting the importance of ending the political division between the Hamas-ruled Gaza Strip and Fatah-controlled West Bank and of standing united in the face of Israeli policies in the occupied Arab lands.
It is Abbas' second visit to Syria since May. His aides have said that Abbas would not meet any Palestinian factions during hisstay in Syria.
Shortly after Abbas met Assad, Hamas leader Khaled Meshaal, who lives in exile in Syria, declared the postponement of delivering a speech initially scheduled for Saturday afternoon, his office told Xinhua by phone.
It, however, did not give the reason behind the delay and when Meshaal is to give his speech that is expected to outline "a new strategy" for the Islamic Hamas movement.
Egypt has set July 7 as a deadline of its mediation between Abbas' Fatah faction and Hamas to produce a Palestinian unity deal.