Speaking to hundreds of supporters via video link, Sheik Hassan Nasrallah said Israel had already accused his militant group of being behind the attack before the Bulgarian report.
Nasrallah also warned the Jewish state against attacking Lebanon, saying Hezbollah's response in such a scenario would be harsh.
The July 18 bombing at an airport in Bulgaria's Black Sea resort of Burgas killed five Israelis as well as a Bulgarian bus driver and the suspected bomber.
Three men are suspected in the attack, including the bomber.
The latter's identity has not been established. The names of the two other suspects, believed to still be alive, have not been made public.
The European Union, of which Bulgaria is a member, which regards Hezbollah as a legitimate political organization and has resisted calls to blacklist the group or declare it a terrorist organization.
Nasrallah's speech was given to mark the anniversary of the death of three Hezbollah leaders, including top military commander Imad Mughniyeh who was killed in a car bomb in the Syrian capital of Damascus in 2008. Hezbollah blamed Israel for Mughniyeh's death and vowed to avenge him.
Nasrallah warned that anyone who thinks Hezbollah is vulnerable because of Syria's civil war is mistaken. He also said that the group has all the weapons it needs in case war breaks out with Israel, and it would not need to import them from allies Syria and Iran.
His comments came two weeks after Israeli warplanes carried out an air raid near Damascus.
U.S. and regional officials said Israel struck a military research center and a convoy carrying sophisticated anti-aircraft missiles from Syria to Hezbollah. Israel has not officially confirmed it carried out the airstrike, though its defense minister this week strongly hinted at Israeli involvement.
The Syrian military denied that the target of the attack was a weapons convoy. It said a military research center was hit.
Israel and Hezbollah have a violent history. The two fought an inconclusive monthlong war in 2006, when Hezbollah fired nearly 4,000 rockets at Israel. Israel's heavy aerial bombardments caused much damage to Lebanese civilian infrastructure but ultimately were unable to stop Hezbollah from continuing to amass a large stockpile of rockets just beyond Israel's northern border.
"The resistance will not be silent regarding any aggression against Lebanon," Nasrallah said. Adding that Hezbollah had the capability to strike at Israel's "ports, airports and power stations."
"A few missiles would plunge Israel into darkness," Nasrallah said, referring to plans to attack power stations. "From Kiryat Shemona to Eilat," Nasrallah said, referring to a northern Israeli town near the Lebanese border, and a southern Red Sea resort.