"I hope his [Abbas'] meetings in Damascus will be constructive and lead to solving all outstanding problems that have broken the dialogue in the past," said Abu Marzouk.
An Abbas aide confirmed that the Palestinian president planned to meet with Meshaal on Monday.
"Unless the US administration is prepared to read the riot act to the Israeli government ... nothing will be achieved"
Nehad Ismail, London, UK
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The secret talks were held between Meshaal and two Abbas envoys, Ziad Abu Amr, an independent legislator, and Mohammed Rashid, a former adviser to Yasser Arafat, the former Palestinian president.
Hamas and Fatah have repeatedly failed in recent months to form a coalition because of disagreements over a political programme and control over key cabinet posts.
Hamas has also balked at international demands that any Palestinian government recognises Israel, renounces violence and accepts existing peace deals.