Syria crisis: Assad issues 'terrorism' vow to Annan
The UN said Mr Annan's task was to call for an immediate ceasefire by the army and the opposition.
As Mr Annan arrived, there were reports of fresh army shelling of the north-western city of Idlib.
Earlier, UN humanitarian chief Valerie Amos said "limited progress" had been made on aid but much more was needed.
Calls for reform that began with pro-democracy protests a year ago have degenerated into violence that has brought Syria to the brink of civil war.
The UN says more than 7,500 people have died as a result of the violence.
'All violence must stop'
Mr Annan's talks with Mr Assad lasted for more than two hours, before Mr Annan met Foreign Minister Walid al-Moallem over lunch.
The Sana news agency quoted Mr Assad as saying: "Syria is ready to make a success of any honest effort to find a solution for the events it is witnessing.
"No political dialogue or political activity can succeed while there are armed terrorist groups operating and spreading chaos and instability."
The BBC's Lina Sinjab in Damascus says this is a clear message that the military operation, and violence, will continue.
As the talks took place, opposition groups said army attacks were continuing on the city of Idlib, near the Turkish border.
The Syrian Observatory for Human Rights said the shelling was the heaviest since army reinforcements arrived earlier in the week and was an apparent prelude to a ground assault, as had happened in the city of Homs.
One activist in Idlib told Reuters by telephone that government tanks were entering the city.
Associated Press reported families fleeing the violence with their belongings.
Mr Ban, the UN secretary-general, earlier spelled out Mr Annan's task.
"Our priority is, first of all, all violence must stop, whether by government forces [or] opposition forces," Mr Ban said.
Mr Annan will reportedly meet the opposition National Coordination Committee early on Saturday evening.
Mr Ban said Mr Annan would hold talks with other opposition leaders after leaving the country on Sunday.
Coinciding with Mr Annan's arrival, a meeting of Arab League foreign ministers has been taking place in Cairo, attended by Russian Foreign Minister Sergei Lavrov.
The BBC's Jon Leyne in Cairo says the meeting has revealed bitter divisions between the League and Moscow, with Russia finding out just how little support its policy on Syria has.
Mr Lavrov warned against "crude interference" in Syria's internal affairs, insisting that Russia was not "protecting any regimes.
Russia's stance on the issue was criticised and the Qatari delegation said it was time to send Arab and international forces in to Syria, as there was a "moral and humanitarian obligation to stop the daily systematic killing there".
Nevertheless the meeting concluded with all sides calling for an end to violence in Syria "whatever its source". A joint statement also set out several points of agreement, which included a rejection of foreign intervention in the conflict-stricken country.
Ministers also agreed on the need for a mechanism to objectively monitor the situation and the need to deliver humanitarian aid.
Mr Ban also echoed Baroness Amos's calls for Syria to allow aid agencies access to areas badly hit by the violence.
He said that what she had seen in the devastated Baba Amr district of Homs showed there was a "quite serious, alarming situation in terms of humanitarian assistance and human rights".
On Friday, Baroness Amos said the government had indicated that an initial humanitarian assessment could be made within the next week, and that a UN team in Damascus was ready to get to work.
Violence continued on Friday across Syria. The Local Co-ordination Committees said 77 people had been killed, including 26 in Homs, 28 in Idlib, six in Deraa, four in Hama, nine in and around Damascus, two in Latakia and one each in Bokamal and Aleppo.