Stepping up political efforts to halt the carnage which monitors say has cost more than 17,000 lives, the UN-Arab League envoy was reportedly to travel on to Iran, Syria's close ally.
The former U.N. chief said he had a 'constructive' meeting with Assad, on his third such mission for talks on his six-point peace plan for Syria since he was appointed in February.
Ahead of his trip to Damascus, Annan admitted his peace blueprint has so far failed to stem the bloodshed in Syria. He also expressed frustration that while Moscow and Iran are mentioned by some as stumbling blocks to peace, 'little is said about other countries which send arms, money, and have a presence on the ground.'
And, in a defiant interview late on Sunday, Assad told German public broadcaster ARD that many countries were undermining Annan's initiative. Assad said the Annan plan had failed because 'many countries don't want it to succeed.'
His decision to travel to Damascus and hold talks with Assad was criticised by the Syrian National Council, the main opposition group in exile which cited the high death toll since they agreed an April 12 ceasefire.
The Syrian Observatory for Human Rights, a monitoring group based in Britain, estimates that 5,898 people have been killed since the truce was announced.
Meanwhile, the Syrian navy staged live fire exercises at the weekend to 'simulate the scenario of repelling a sudden attack from the sea,' state news agency SANA reported.
On the ground Monday, the Syrian army clashes with rebels in several main cities across the country, including the capital Damascus, Deir Ezzor in the east and Homs in central Syria, the Observatory said.