In a speech to his supporters on Saturday, Nasrallah condemned US policy in the Middle East, saying it was misguided and, in a reference to Israel, that it only served the "cancerous entity".
Nasrallah's public appearance comes amid heightened tension in Lebanon, which has been without a president for nearly two months because of a crisis between the Western-backed parliamentary majority and the Hezbollah-led opposition.
Addressing his supporters, Nasrallah reiterated that Hezbollah supported an Arab League plan to resolve the crisis.
The plan envisages General Michel Suleiman, the former army chief, in place as president, a national unity government in which no one party has veto power and the adoption of a new electoral law.
But the Hezbollah leader criticised Arab leaders who have been pushing the plan, saying they should refrain from giving lessons about democracy.
"I find it strange that Arab leaders speak about ... democracy when their own regimes know nothing about it," he said.
Speaking about his group's war with Israel in 2006, he claimed Hezbollah had forced the Israeli army to beat a retreat and warned that his group stood ready for a new conflict.
"If Israel launches a new war against Lebanon, we promise them a war that will change the face of the entire region," he said.
During his speech, Nasrallah also claimed that Hezbollah had the remains of Israeli soldiers killed in Lebanon during the 2006 war.
"Your [Israel's] army left behind the remains of soldiers in our villages and fields," he said.
"They [Israeli army] were so weak on the field that they left behind remains not of one, two or three but a large number of your soldiers," Nasrallah said.
"One body is almost complete," Nasrallah said. "What did the [Israeli] army say to the family of this soldiers and what remains did they give them?"
Religious and political
Thousands of men, women and children dressed in black had gathered in Beirut for to commemorate the Ashura ceremony, many punching their fists in the air and beating their chests in unison.
Some chanted "We serve you Hussein", as a sign of grief at the killing of Imam Hussein, the grandson of the Prophet Muhammad.
At the same time, Hezbollah supporters carrying red, yellow and black banners with the slogan "We will not be humiliated" marched in procession, blocking suburban roads, chanting "Death to America, Death to Israel".
Ashura is the 10th day of the lunar month of Muharram when according to Islamic tradition, Hussein was killed along with most of his family in 680AD in the Iraqi city of Karbala.
Hussein's death is a defining moment in the history of the Shia interpretation of Islam.