"The government wants to raise brotherly ties between Lebanon and Syria to a level in line with the two countries' historical ties and mutual interest," al-Hariri said before his new cabinet received parliament's vote of confidence.
In the past, al-Hariri has implicated Damascus in his father's killing in a Beirut bombing in February 2005. He has never had any official contact with al-Assad's government.
Al Jazeera's Rula Amin, reporting from Damascus, said the visit was a pragmatic decision by the Lebanese PM to recognise a changing political landscape.
"For the premier to come here as a guest of the Syrian government is a huge step ... it shows he is willing to play his part in bringing Damascus out of its regional and international isolation.
"This trip would not have been possible if Syria had not mended its relations with Saudi Arabia and improved ties with the United States", Amin said.
The international community has also largely pinned the blame for the assassination on Syria, pressure that ultimately ended Syria's 29 years of occupation in Lebanon.
But Damascus has consistently denied involvement in the assassination, and 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 UN has not brought charges against Syria over Rafiq al-Hariri's assassination [AFP]
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.