Buthaina Shaaban, an adviser to al-Assad, said talks between the two leaders on Saturday were "frank" and "succeeded in overcoming difficulties that marred relations in the past five years".
"The guarantee to that is the will of both President Assad and Hariri to build a positive and constructive relationship," she said.
'Personal beliefs aside'
Al Jazeera's Rula Amin, reporting from Damascus, said the visit indicates that the political landscape in the region has changed.
"Syria has reasserted itself as a regional indispensible player. And as [al-Hariri] assumed power of Lebanon he said he feels that there is a need to improve relations with Syria and that is why he is here," she said.
|The UN has not brought charges against Syria over Rafiq al-Hariri's assassination [AFP]
"His personal beliefs on who killed his father are put aside and he is here as a politician.
"For many Lebanese who are shocked by this, they feel that, on this visit, Saad al-Hariri has been baptised as a politician.
"For many, it's a disappointment. Other people feel that the stability and security of Lebanon requires and warrants such a visit and by doing so, he is proving to be a good politician."
The international community has largely pinned the blame for the assassination of al-Hariri's father on Syria.
Syria pulled its troops and security officials out of Lebanon in April 2005, after thousands of Lebanese held street protests to charge that Damascus had a hand in the killing.
But Damascus has consistently denied involvement in the assassination.
While a UN inquiry has said it has evidence that Syrian and Lebanese intelligence services were linked to the killing, no charges have ever been brought.
Earlier this month, a Syrian court asked 25 prominent Lebanese figures, including individuals close to al-Hariri himself, to appear for questioning over the murder.
The Syrian court acted after Jamil Sayyed, the former Lebanese security services director, filed a lawsuit in October regarding his four-year detention without charge over Rafiq al-Hariri's murder.
The list also included Ashraf Rifi, a former Lebanese police chief and the prosecutor general, Saeed Mirza, as well as several MPs and journalists.
The initiative to improve relations between Lebanon and Syria began in 2008 with an exchange of ambassadors.
Syria opened its first embassy in Lebanon just under a year ago, and Lebanon sent an ambassador to Damascus in March.
It was the two countries' first diplomatic exchange since gaining independence from France more than 60 years ago.
The Syrian president also welcomed the Lebanese president, Michel Sleiman, to Syria on Friday.