UN-Arab League envoy Kofi Annan, on a two-day peace mission to Damascus, is due to hold a second round of talks with Syrian President Bashar al-Assad.
On the first day of talks, President Assad rejected any political dialogue while "armed terrorist groups" were operating in the country.
Mr Annan is trying to arrange a ceasefire and gain greater access for humanitarian aid agencies.
He will later travel on to neighbouring countries, the UN says.
Diplomatic sources say his first port of call may well be Turkey, which has taken a tough line against President Assad's deadly crackdown.
President Assad is trying to crush a increasingly armed rebellion that sprang from the harsh crackdown of peaceful pro-democracy protests.
The UN says more than 7,500 people have died since unrest began a year ago.
Fighting on Saturday left at least 63 people dead, activists said, with heavy shelling reported in the northern town of Idlib.
'Candid and comprehensive'
Syrian state TV said Mr Annan's first round of talks took place in a "positive" atmosphere.
Mr Assad is reported to have said: "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."
A spokesman for Mr Annan called the talks "candid and comprehensive".
On Saturday Mr Annan also met leaders of some Damascus-based opposition groups, including Hassan Abdulazim, head of the Syrian Opposing Co-ordination Body.
"We asked Kofi Annan to co-ordinate with the Arab League and its efforts," said Mr Abdulazim.
"We thanked him for UN efforts to find a solution for the crisis in Syria. Any negotiation for finding a transitional phase should be conducted after stopping violence, releasing prisoners and establishing a suitable environment."
International disagreements have paralysed action on Syria, with Russia and China opposing Western and Arab calls for President Assad to stand down.
The US has drafted a fresh UN Security Council resolution but the State Department said on Friday it was not optimistic that the text would be accepted.
Although the UN wants "inclusive political solutions" through dialogue, Syrian opposition leaders have rejected talks while President Assad is still in power.
Meanwhile, fierce fighting was reported from the north Syrian town of Idlib on Saturday, where fighters from the Free Syrian Army were trying to hold back government forces.
"Regime forces have just stormed into Idlib with tanks and heavy shelling is now taking place," an activist told Reuters by telephone.
The UK-based Syrian Observatory for Human Rights said 16 rebel fighters, seven soldiers and four civilians had been killed in Idlib on Saturday.
Tight restrictions on foreign journalists inside Syria mean the figures cannot be verified.