Annan met Bashar al-Assad, the president, in Damascus on Friday. The UN chief had arrived in Syria on Thursday and met Walid al-Mualim, the foreign minister.
Ahmad Fawzi, Annan's spokesman, said: "It was a very good meeting. The president and Mr Annan discussed the implementation of security council resolution 1701 and the president told Mr Annan that Syria supports and will help its implementation."
Asked whether Annan and al-Assad's talks covered Lebanese-Syria border issues, Fawzi said: "Yes, they discussed everything."
UN resolutions have called on Syria to demarcate its borders with Lebanon, including in the Israeli-occupied Shebaa Farms area, claimed by Beirut, with Syria's verbal backing, but viewed by the United Nations as Syrian territory.
Israel, however, reacted with scepticism to Syria's commitment to stop the flow of weapons to Hezbollah.
"Israel does not think that Syria during the last conflict - both in helping Hezbollah by financing and arming them directly and the declarations during the conflict - and in its aftermath, has shown any reason to be a reliable force," government spokeswoman Miri Eisin said.
"Syria continues to be a safe haven for terrorism."
Al-Assad has previously said there will be no demarcation in the Shebaa Farms while it is occupied by Israel.
Annan had been expected to urge al-Assad to stop backing Hezbollah, whose main allies are Syria and Iran.
The UN chief told the Lebanese government at the start of his tour that he would press Syria to open an embassy in Beirut and conduct normal diplomatic relations with Lebanon.
Syria has long dismissed this as unnecessary between two closely linked neighbours, prompting Lebanese suspicions that Damascus refuses to acknowledge as fully sovereign the country it dominated until it ended a 29-year troop presence last year.
Annan had been expected to ask
Syria to stop arming Hezbollah
"They also discussed all tracks of the peace process," Fawzi said, referring Israel's stalled negotiations with Syria and the Palestinians over territory occupied by Israel in the 1967 war.
Al-Assad had been expected to urge Annan to promote a wider peace in the region, as well as in Lebanon.
Even before the Lebanon war, Syria was under pressure from an earlier UN resolution which had demanded the disarming of all militias in Lebanon - Hezbollah and Palestinian groups.
A UN inquiry into last year's killing of Rafiq al-Hariri, a former Lebanese prime minister, initially pointed the finger at Syrian security officials. Its chief investigator, Serge Brammertz, is due to submit a new report later this month.
Syria has denied any part in the assassination of al-Hariri.