“The outcome of this war is clear: Saudi Arabia will be defeated and the Yemeni people will have an undeniable victory,” Nasrallah said in a televised speech.
Hezbollah is now militarily involved in Syria, where it is bolstering the embattled regime, and in Iraq where it says it is fighting Sunni extremists.
A months-long rebellion by Shiite fighters in Yemen escalated into a regional conflict Wednesday, when a coalition led by Saudi Arabia began conducting air strikes on rebel-held territory.
Hezbollah firmly criticised the operation, calling it “unjust” and “illegal”.
“It is the right of the oppressed… Yemeni people to resist and defend… and that is what they are doing,” Nasrallah said Friday, calling for a political solution to the conflict.
The Hezbollah chief launched into a strongly worded diatribe against the Saudi kingdom, accusing it of launching air strikes against Yemen to “regain its hegemony” over the country.
“The problem is you — you failed. Your way of doing things failed,” he said, addressing the Saudi leadership.
“Saudi leaders have one last chance before they are defeated and humiliated, and that is to behave with the Yemenis like brothers and to begin a dialogue while the door is still open,” Nasrallah said.
He called on the Arab League, “instead of being complicit in the bloodshed in Yemen, to assume a historic responsibility by stopping this aggression and moving towards a political solution.”
“Otherwise, defeat and shame will meet the invaders,” Nasrallah warned.
A two-day Arab League meeting from Saturday in Egypt’s Red Sea resort of Sharm el-Sheikh is expected to be dominated by the Yemen crisis.
Nasrallah spoke for a little over an hour on Hezbollah’s Al-Manar television station, which has been closely covering the situation in Yemen.
Since its founding in the 1980s in Lebanon, Hezbollah has been financially and politically supported by the Islamic republic of Iran.