Hezbollah launched an anti-tank missile on Sunday and Israel exchanged fire.
"The red line which Israel has established on its borders with Lebanon was broken and if Lebanon is attacked all your soldiers and your settlements will be at risk," Nasrallah said as he was addressing a crowd via a video link during a religious ceremony.
He said Sunday's strike against an Israeli military vehicle has initiated a new phase and that the attack was done in the middle of the day despite heavy Israeli monitoring of the Lebanese border.
The movement has said the missile strike was a response to an Israeli attack which targeted Hezbollah militants in Syria last month. Israel said at the time that the attack thwarted an Iranian attempt to hit Israeli targets using "killer drones."
"We said it openly a week ago that we will retaliate," the Hezbollah chief said.  
He reiterated that Lebanon has the right to protect its sovereignty and its people.
Shortly before Nasrallah spoke, his Lebanon-based militant group broadcast video footage showing the actual firing of the rockets in Sunday's attack.
Hezbollah's Al Manar television showed the Israeli Avifim military base, near the Israel-Lebanon border, then the cameraman zoomed out to show a Hezbollah missile launcher on the Lebanese side being fired towards the Israeli target.
The footage then showed an Israeli Wolf armoured vehicle driving up a road alongside the Avifim settlement, before being hit by the missile.
The militants say the attack has caused casualties among the Israeli army, but Israeli Prime Minister Benjamin Netanyahu denied this, stating there were no injuries.
Nasrallah warned that any Israeli drone which violates Lebanese airspace will be confronted from now on.
Tensions have spiked in the region since August 25, when Hezbollah said two Israeli drones went down over Beirut's southern suburbs.
"The operation of the drones failed to hit its targets. We tell the enemy your operation has failed," Nasrallah said.
Israel's Foreign Ministry said in a statement that Katz had asked German Foreign Minister Heiko Maas to convey the following message to Beirut: "If you do not stop Hezbollah's activities against Israel, then all of Lebanon will suffer damage and be severely affected."
Katz said Israel did not want an escalation in violence but that his country "is prepared to continue to react harshly to any attack and sees the state of Lebanon as the only responsible party."
Germany is acting as a go-between and the Foreign Ministry in Berlin said Maas had telephoned counterparts in Lebanon and in Israel in recent days. Maas told Beirut that a moderating influence was needed on Hezbollah.
Israel's Katz has called for German sanctions against the militant group and demanded that Berlin classify Hezbollah as a terrorist organization.
Calm had returned to the Lebanese-Israeli border on Monday, following Sunday's burst of violence.
According to United Nations sources, members of the United Nations Interim Forces in Southern Lebanon (UNIFIL) were patrolling the land around Maroun al-Ras, which was hit by more than 40 incendiary and cluster devices from Israel.
Israel has said Iranian officers are working with Hezbollah in Lebanon to advance an effort to convert rockets into precision-guided missiles.  
------------------------------------------------------------------------------------------