Its response to any future Israeli attack will no longer be limited to Lebanese territory, he warned in an address via video link to thousands of supporters gathered in Hezbollah's southern Beirut stronghold.
He said Hezbollah would no longer respect "the rules of engagement".
"We do not want war... But the resistance is militarily ready, and we are not afraid of war," Nasrallah said, using the term "resistance" to refer to Hezbollah.
The strike was in retaliation for a January 18 Israeli air strike inside Syria that killed six Hezbollah fighters and an Iranian general.
"I want to be clear: the resistance will no longer recognise any such thing as the rules of engagement, or of confrontation," said Nasrallah, appearing both defiant and relaxed.
"It is our right -- legally, in human terms and morally -- to face the enemy anywhere, any time and in any way we deem appropriate," he warned.