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 northwestern 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 reponse 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."
Ban said his predecessor would seek to encourage dialogue between Assad's government and the opposition but that he would not meet opposition figures inside Syria on his two-day visit.
As the Annan mission was starting, Syrian troops heavily shelled the northwestern protest city of Idlib in an apparent prelude to a ground assault, a watchdog said.
Security force fire killed two civilians in the province on Saturday, while 23 rockets slammed into the Idlib town of Saraqeb, wounding four civilians, one of them seriously, the Observatory said.
Near the capital, two loyalist soldiers and three rebel troops were killed in dawn clashes in the town of Daraya. The army deployed reinforcements and civilian was killed in the crossfire, the Observatory added.
Annan's visit comes a day after UN humanitarian chief Valerie Amos left Damascus following a hard-won but troubled mission to secure relief access to besieged protest centres.
Speaking in Ankara on Friday, Amos said a "joint preliminary humanitarian assessment mission" had been agreed, to provide assistance to people urgently in need of it.
In Cairo, Lavrov reiterated Russia's opposition to an Arab- and Western-backed draft Security Council resolution that it has dubbed "unbalanced" because it does not contain a call for a simultaneous halt to violence by government forces and the rebels.
He told his Arab counterparts that violence in Syria must end, "irrespective" of its origin.
But Qatari Foreign Minister Sheikh Hamad bin Jassim al-Thani voiced exasperation with the position of Russia and China, saying the killings of civilians in Syria amounted to "genocide" and that a ceasefire was "not enough."
"Our patience and the patience of the world has run out," he said.