"With this murder, its timing, location and method - Zionists [Israel] if you want this kind of open war, let the whole world listen: let this war be open," he said.
He said Hezbollah fighters had started preparing for the next war immediately after the end of the 2006 war with Israel.
Speaking in a videotaped message to supporters at the funeral service for Moghaniyah in southern Beirut on Thursday, Nasrallah said: "Like all human beings we have a sacred right to defend ourselves.
"We will do all that it takes to defend our country and people."
Israel on alert
The Israeli prime minister's office issued a warning late on Thursday urging Israeli citizens to act with extra caution while abroad, noting the threat of kidnapping.
It advised staying out of Arab and Muslim countries, avoiding concentrations of other Israelis and turning down "unexpected invitations to meetings in remote places".
Lieutenant-General Gabi Ashkenazi, Israel's military chief, put forces on heightened alert, and the military sent more troops to the already fortified border with Lebanon, defence officials said.
Israeli embassies worldwide also were put on alert, and Israeli security forces advised Jewish institutions across the globe to be vigilant, officials said.
In Washington, Sean McCormack, the US state department spokesman, called Nasrallah's threats "quite concerning".
"Quite clearly, Hezbollah has a long record of carrying out violent acts and acts of terrorism around the globe," he said.
The speech by Nasrallah, who is in hiding after the July 2006 war between Israel and Hezbollah, came shortly after an event elsewhere in the Lebanese capital to mark the third anniversary of the assassination of Rafiq al-Hariri, a former prime minister.
Thousands of other Lebanese called on Syria
to stay out of their country's politics [AFP]
Security was tight as thousands of people gathered for the two separate rallies, which highlighted the deep divisions in the country.
Leaders in the pro-government March 14 bloc had supporters in the al-Hariri commemoration in Martyrs Square to show their rejection of alleged Syrian efforts to regain influence in Lebanon.
Hezbollah, which is supported by Syria and Iran, has led an opposition political bloc against March 14 for the past three years.
Rula Amin, Al Jazeera's correspondent in Beirut, said the rallies advanced different visions for Lebanon.
She said the al-Hariri rally speakers took pride in the fact that it was the US, the EU and the West that was backing them.
But in the southern suburbs, at the funeral for Moghaniyah, there was defiance against Israel, the US and the West in general which considered Moghaniyah a terrorist, she said.
The funeral was a message from Hezbollah not just to Israel but the March 14 leaders that the Shia group also commanded support on the streets, Amin said.
Moghaniyah, who was accused by the US of planning attacks on Western targets during the Lebanese civil war, was killed by a car bomb in Damascus on Tuesday evening.
Nasrallah said that the death of Moghaniyah would only strengthen the resistance against Israel.
"Moghaniyah's blood will lead to the elimination of Israel. These words are not an emotional reaction," he said.
Amin said Nasrallah's words had left many Lebanese wondering if there will be another war with Israel.