The US has said it welcomes the killing of a top Hezbollah commander implicated in numerous bomb attacks and a wave of hostage-taking in Lebanon in the 1980s.
Mughniyeh was wanted in connection with a series of attacks
A US state department spokesman said the world would be a "better place" without Imad Mughniyeh, whom he called a "mass murderer and a terrorist".
But Sean McCormack said he did not know who was responsible for the car bombing overnight in Damascus that killed him.
Hezbollah and Iran have blamed Israel, but it has denied any involvement.
The Syrian government also condemned the "cowardly terrorist act" and said investigations were still underway to find the perpetrators.
Mughniyeh, in his late 40s, had been variously described as special operations or intelligence chief of Hezbollah's secretive military wing, the Islamic Resistance.
Correspondents say his death will be a significant blow to Hezbollah, which battled Israel in the 2006 Lebanon war, with help from its Iranian and Syrian backers.
Mughniyeh had been top of the US Most Wanted list until he was replaced by Osama Bin Laden and other al-Qaeda leaders following the 11 September 2001 attacks.
He was alleged to have been involved in the killings of more Americans than anyone else in the world, including the 1983 bombing of the US embassy in Beirut and the UN compound, in which 241 US Marines and 58 French paratroopers died.
The US government also placed a $5m bounty on his head after he was indicted for his alleged role in planning and participating in the hijacking of a TWA commercial airliner in 1985, during which a US navy diver was murdered.
After the confirmation of Mughniyeh's death on Wednesday morning, state department spokesman Sean McCormack said the US did not know who had been responsible for the bombing, but applauded it nonetheless.
"The world is a better place without this man in it," he told reporters.
Born southern Lebanon 1962
Indicted for 1985 hijack of TWA airliner
Accused of involvement in 1990s Buenos Aires bombings
On FBI Most Wanted list since 2001
"He was a cold-blooded killer, a mass murderer and a terrorist responsible for countless innocent lives lost," he added. "One way or another he was brought to justice."
Mr McCormack said list of other nationalities who had been affected by Mughniyeh's "acts of terror" went "on and on and on".
Israel believes he was involved in planning the 1992 bombing of its embassy in Argentina in which 29 people were killed, and the blast at a Buenos Aires Jewish centre two years later that killed 95.
Syrian police kept media and other onlookers well away from the scene of the overnight blast in the well-to-do Kafar Soussa district.
Witnesses saw security officers hauling the body away from a burnt-out vehicle.
On Wednesday morning, Hezbollah-owned Manar TV announced that one of the group's senior commanders had been killed.
"With all pride we declare a great jihadist leader of the Islamic resistance in Lebanon joining the martyrs... the brother commander hajj Imad Mughniyeh".
"After a life full of jihad, sacrifices and accomplishments... he died a martyr at the hands of the Israeli Zionists," a Hezbollah statement said.
Later, the Syrian government confirmed Mughniyeh had been killed and said investigations were still underway to find the perpetrators.
"Syria, which condemns this cowardly terrorist act, expresses condolences to the martyr family and to the Lebanese people," Interior Minister Bassam Abdul-Majeed said in a statement.
Iran also condemned the killing, praising Mughniyeh as a martyr and describing the attack as "yet another brazen example of organised state terrorism by the Zionist regime".
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The Israeli government, which has been accused of a series of assassinations of its enemies in various countries over the years, stopped short of an outright denial that it had killed Mughniyeh.
"Israel rejects the attempt by terror groups to attribute to it any involvement in this incident," Prime Minister Ehud Olmert's office said in a statement.
Hezbollah said a funeral service would be held in its stronghold in the southern suburbs of Beirut on Thursday.
The city has been tense ahead of a mass rally also on Thursday to commemorate three years since the assassination of former Prime Minister Rafik Hariri.
Hezbollah was founded in 1982 by a group of Shia Muslim clerics after the Israeli invasion of Lebanon. It has emerged in recent years as a major political and military force in Lebanon, after military successes against Israel.