State television said there was a "positive atmosphere" to the Damascus meeting between Assad and the former UN chief, on his first visit since being named United Nations-Arab League envoy on the conflict.
Annan himself made no public comment about the progress of his crux mission to prevent a year-old uprising from spiralling into all-out civil war.
"Syria is ready to bring success to any honest bid to find a solution," the official SANA news agency quoted Assad as telling Annan.
But "no dialogue or political process can succeed as long as there are terrorist groups that are working to sow chaos and destabilise the country by attacking civilians and soldiers," he added.
"The success of any effort firstly requires an examination of what is happening on the ground instead of presumptions spread by certain states of the region and others to distort the reality ... of the situation in Syria," said Assad.
The meeting came against a backdrop of fierce fighting between troops and rebel fighters, particularly in the north-western province of Idlib, close to the border with Turkey, where the Free Syrian Army has been especially active.
Troops killed 16 rebels in an ambush in the province on Saturday while the rebels killed four soldiers and captured five, the Syrian Observatory for Human Rights said.
Nationwide, 31 people were killed, the Britain-based watchdog said, adding to a death toll that had already topped 8 500 since protests against Assad's regime erupted last March.
Emissary of the United Nations and the Arab League, Annan has the support of Damascus allies Beijing and Moscow and his mission has been welcomed by the both the Syrian government and opposition.
But Russia said its Foreign Minister Sergei Lavrov made clear to Annan at a meeting earlier in Cairo that Moscow was opposed to "crude interference" in Syria's affairs.
"A particular emphasis was placed on the inadmissibility of trampling on international legal norms, including through crude interference in Syria's internal affairs," the foreign ministry said.
The Russian stance drew an angry response from Gulf states when Lavrov joined an Arab foreign ministers' meeting in Cairo with Saudi Arabia's Saud al-Faisal accusing Moscow of giving Damascus a "licence to extend its brutal practices against the Syrian people, without compassion or mercy."
Current UN chief Ban Ki-moon said Annan would demand an immediate end to the violence and aid agency access to besieged protest cities to evacuate casualties and provide desperately needed relief supplies to civilians trapped by the fighting.
"I very strongly urged Kofi Annan to ensure there must be an immediate ceasefire," Ban said. "I also asked him to urge Assad to facilitate humanitarian assistance and access."