"We will continue our efforts for dialogue."
Sarkozy had called on al-Assad to urge Iran, which has ties with Syria, to urge Tehran to co-operate with Western powers over its nuclear programme.
The West has sought to curb Iran's nuclear ambitions, fearing Iran could develop a nuclear weapon. Tehran, though, says its nuclear plans are for purely civilian purposes.
The United States and Israel have refused to rule out military action if the dispute cannot be resolved through diplomacy.
Sarkozy said: "Iran having the atom bomb is a threat to peace in the region and to peace in the world. Everyone must get the message across in their own way."
Sarkozy's visit to Damascus is the first by a Western head of state since the murder of Rafiq al-Hariri, the Lebanese prime minsiter, five years ago. Syria's critics accuse Damascus of being behind al-Hariri's assassination, a charge Syria has denied.
Al-Assad said Sarkozy's trip heralded a new era in relations between the two countries.
For his part, Sarkozy appears determined to bring Syria back into the international fold, despite hostility from other Western powers including the US.
Relations between Paris and Damascus have started to improve since Sarkozy hosted al-Assad in France in July.
France has promised al-Assad economic incentives in return for political progress.
Accompanying Sarkozy on his visit is Christophe de Margerie, the chief executive officer of French oil company Total, which is in talks to expand an oil licence in Syria.
During his visit Sarkozy is also expected to court Syrian co-operation on Lebanon.
Syria has long been involved in Lebanon, only withdrawing its troops there in 2005 following protests prompted by al-Harriri's murder.
France has accused Syria of contributing to the crisis in Lebanon, which turned violent in May before a Qatari-brokered deal resulted in the formation of a national unity government in which the Hezbollah led-opposition has veto power.
"Anything concrete on Lebanon will be a triumph for Sarkozy. He needs something to justify to more sceptical Europeans that engagement with Syria works," a diplomat in Damascus said.
Al-Assad and Sarkozy will join Tayyip Erdogan, the Turkish prime minister, and Sheikh Hamad bin Khalifa al-Thani, Qatar's emir, on Thursday for talks on Lebanon and to disucss Syria's talks with Israel, which are being mediated by Turkey.
The fifth round of the Turkey-brokered talks is expected to be held in Ankara, the Turkish capital, on Sunday.