People converged on Al-Mujtaba compound in the neighborhood of Sfeir in Beirut’s southern suburbs to praise the late commander.
Speaker Nabih Berri expressed his condolences in a phone conversation with Hezbollah secretary-general Sayyed Hasan Nasrallah.
"It is the martyrdom that the great leader deserved and it will remain an open war," Hezbollah MP Nawar Sahili told Al-Manar TV network.
He preferred to "wait for the investigation conducted by the resistance" before accusing any side of the assassination, the Daily Star reported.
Hezbollah said Badreddine had died in a "big explosion" that targeted one of its bases near Damascus airport. It said it was working to "define the nature of the explosion and its cause, and whether it was the result of an airstrike, or missile or artillery."
It did not say when the attack happened.
Unconfirmed reports had said an Israeli air raid targeted a Hezbollah arms convoy on the border near the Beirut-Damascus highway Tuesday night. Hezbollah at the time denied the reports.
There was no immediate comment from Israel.
Hezbollah MP Ali Miqdad also mourned Badreddine, whose nom de guerre was Zu al-Fiqar, as "a man of great achievements."
Industry Minister Hussein Hajj Hassan said that Badreddine's "martyrdom will stimulate [the resistance] to remain on the path of jihad."
Hezbollah said it would hold Badreddine's funeral at 5:30 p.m. local time Friday in the southern Ghobeiri suburb.