The former UN chief said they had a "constructive" meeting on his third such mission for talks on his six-point peace plan since his appointment in February.
Syrian foreign ministry spokesman Jihad Makdissi also called the meeting "constructive and good."
Pro-government Al-Watan newspaper said the talks focused on the results of the Geneva meeting at the end of June of an international contact group on Syria.
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."
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.
Monday's meetings came as at least 58 people were killed nationwide, the Syrian Observatory for Human Rights said, a day after nearly 100 people died.
The army pounded besieged rebel-held areas of Homs, monitors said, 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 that is a key point of the envoy's plan.
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."
-- Iran has key role to play --
Later on Monday Annan flew to Tehran for talks with Saeed Jalili, Iran's top security official, and Foreign Minister Ali Akbar Salehi.
Annan's spokesman Ahmad Fawzi said the envoy would discuss Syria in light of the Geneva meeting "and to see how we can work together to help settle the situation in Syria."
Annan has said Tehran has a key role to play in efforts to end the bloodshed.
Iran was not invited to the Geneva talks, despite Annan's wishes, because of US and EU objections.
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.
On Sunday US Secretary of State Hillary Clinton warned time was running out to save Syria from a "catastrophic assault."
"It should be abundantly clear to those who support the Assad regime their days are numbered," she said.
British Foreign Secretary William Hague called for a "strong commitment" from Russia to support Annan's peace plan, and again insisted that Assad must quit.
"We now want to see Kofi Annan's plan fully implemented -- we believe there can be no future for Syria with Assad in power and there must be a Syrian-led political process," Hague said.
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.
The Observatory, a Britain-based monitoring group, estimates that 5,898 people have been killed since the Annan-brokered April truce.
On Monday at least 28 civilians, 24 regime troops and six rebels were killed across Syria, the Observatory said.
Monitors and activists said the army pounded besieged rebel-held districts of the central city of Homs, and Qusayr.
Troops have pounded Qusayr continuously for three months and attacked in the early morning to "terrorise" people and cause maximum casualties as civilians are out and about, an activist identifying himself as Hussein said.
An AFP correspondent saw several members of one family being treated for wounds, including a 13-year-old boy, his T-shirt soaked in blood, after a shell exploded 10 metres (yards) away.