Jumblatt expressed his willingness to open a new chapter with Syria, the country that many in Lebanon hold responsible for the murder of his politician father, Kamal Jumblatt in 1977.
Damascus has also been blamed by many for the 2005 assassination of Rafiq al-Hariri, the former Lebanese prime minister.
'Turn the page'
Asked whether he was willing to visit Damascus, he said his visit to Syria depended on Syrians' willingness to move on.
He said: "I call on the Syrian leadership; for the sake of nation's (Arab nation) interest, regional interests, Arab objective dialogue, objective Syrian-Lebanese relations and the ties between the two neighbouring countries, can he (President al-Assad) rise above this issue? I simply ask for this."
"Yes, I want to turn the page," he stressed.
After joining the March 14 movement, Jumblatt had pressed for the withdrawal of Syrian forces from Lebanon following al-Hariri's murder.
Under intense pressure, Syria withdrew its troops from Lebanon in April 2005, ending three decades of military presence in its smaller neighbour.
Jumblatt has since split from the March 14 movement.