"We discussed the need to end the violence and ways and means of doing so. We agreed an approach which I will share with the armed opposition," UN-Arab League envoy Annan said after meeting Syria's President Bashar al-Assad in Damascus on Monday.
Syrian foreign ministry spokesman Jihad Makdissi called the meeting "constructive and good".
Stepping up efforts to halt the carnage which monitors say has cost more than 17,000 lives, Annan then travelled on to Iran, Syria's closest regional ally, in his quest to broker a solution.
The diplomatic efforts were carried out against the increasingly familiar backdrop of bloodshed in Syria, with the United States and the European Union expressing concern at the outbreak of cross-border clashes with Lebanon.
Shells fired from Syria landed overnight in northern Lebanon after an exchange of fire along the border, a senior Lebanese security official told AFP early Tuesday.
The Syrian shells were fired into Lebanon following a cross-border gun battle, the source added.
There was no immediate report of casualties, but the latest incident came just two days after border clashes in which two girls were killed and several other people wounded in Lebanon.
US Ambassador to Lebanon Maura Connelly on Monday called on Damascus to "respect the sovereignty and territorial integrity of Lebanon".
In Brussels EU foreign policy chief Catherine Ashton's office released a statement saying she "strongly condemns the recent shelling of the Lebanese border area by Syrian artillery, causing several deaths and injuries".
Monday's interventions also came as at least 58 people were killed nationwide, the Syrian Observatory for Human Rights said, a day after nearly 100 people died.
Pro-government Al-Watan newspaper said Annan's discussions focused on the results of the Geneva meeting at the end of June.
They discussed means "to implement the results of the meeting... on forming a transitional government in Syria that groups government and opposition representatives without mention of Assad's departure", it said.
World powers in Geneva agreed a plan for a transition which did not make an explicit call for Assad to quit, although the West and the opposition made clear it saw no role for him in a unity government.
On the ground in Syria, the army pounded besieged rebel-held areas of Homs, monitors said Monday, as Qusayr also came under a morning bombardment.
The opposition Syrian National Council (SNC) slammed Annan's decision to meet Assad, saying thousands of people have been killed despite an April ceasefire.
Annan, whose military observers in Syria have been grounded because of escalating violence, admitted in remarks published by French newspaper Le Monde ahead of his Damascus trip that his peace blueprint has so far foundered.
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".
Moscow arms export officials said Monday that Russia will not supply new weapons to its Arab ally Syria while fighting there continues, while stressing that old contracts would be fulfilled.
Earlier, Russian President Vladimir Putin said Syria needed dialogue between the regime and opposition, rather than foreign intervention, to ensure a lasting peace.
Putin spoke after prominent Syrian opposition leader and intellectual Michel Kilo met Foreign Minister Sergei Lavrov in Moscow.
Later on Monday Annan few to Tehran for talks with Saeed Jalili, Iran's top security official, and Foreign Minister Ali Akbar Salehi.
Annan has said Tehran has a key role to play in efforts to end the bloodshed.
Iranian President Mahmoud Ahmadinejad has accused the United States and its allies of opposing Assad's regime with the goal of dominating the Middle East and propping up Israel.
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It's doubtful if Annan could get Iran to broker a peaceful solution. Assad is Iran's closest regional ally and Tehran will do everything to keep him in power, by sending ihm arms and military personal to quell the opposition. Russia might be a better choice for the West. Yet it's uncertain how much influence the Russians still have on Assad.