Thousands of people have attended the funeral in Lebanon's capital, Beirut, of top Hezbollah military commander Mustafa Amine Badreddine.
He died in an explosion near Damascus airport, the Lebanon-based group said.
An initial report by Lebanon's al-Mayadeen TV said that Badreddine, 55, had died in an Israeli air strike. But a later statement by Hezbollah on al-Manar's website did not mention Israel.
Hezbollah has sent thousands of troops to support Syria's President Assad.
Badreddine is believed to have been a senior figure in Hezbollah's military wing. In 2015, the US said he was behind all Hezbollah's military operations in Syria since 2011.
He was also charged with leading the assassination of former Lebanese PM Rafik Hariri in Beirut in 2005.
He was a cousin and brother-in-law of Imad Mughniyeh, who was the military wing's chief until his assassination by car bomb in Damascus in 2008.
Images from the funeral showed the coffin being carried among a mass of supporters in the southern suburbs of Beirut, some of them chanting "Death to America" and Shia slogans.
Israel's government traditionally refuses to comment on such deaths and has done so again.
But Israel has been accused by Hezbollah of killing a number of its fighters in Syria since the conflict began.
The group was established in the wake of the Israeli occupation of Lebanon in the early 1980s, and has called for the "obliteration" of Israel.
Asked who might have carried out the attack, Hezbollah deputy leader Sheikh Naim Qassem said that, within hours "we will announce in detail the cause of the explosion and the party responsible for it", adding there were clear indications of those responsible.
One Hezbollah MP in Lebanon, Nawar al-Saheli, said: "This is an open war and we should not pre-empt the investigation but certainly Israel is behind this. The resistance will carry out its duties at the appropriate time."
However, any of the armed groups seeking to overthrow President Bashar al-Assad might have have sought to kill the man co-ordinating Hezbollah military activities.