Addressing a massive Dussehra gathering at the Aishbagh Ram Leela ground here, Modi said terrorism in all forms was anti-humanity and Hindu Lord Rama represented all that was human.
It was the Prime Minister's first public speech after the September 29 surgical strikes by the Indian Army at terror launch pads in Pakistan-administered Kashmir.
He made no direct reference to the surgical strikes or to Pakistan that killed an unspecified number of terrorists but made it more than clear which country he had in mind.
"Those who spread terrorism need to be annihilated and those who aid terrorism will not be spared either," Modi said in a speech laced with references to Hindu religion.
Modi said India was a country that respected both Lord Krishna who led the Pandavas in the war of Mahabharata and Mahatma Gandhi who propagated non-violence.
"We are the people who go from yuddha (war) to Buddha (peace). Sometimes war is necessary, but our path is not that of war, but that of Buddha.
"We create balance... I hope the path shown by Buddha will be our final path," he said.
Modi invoked Ramayana and asked his countrymen to keep a vigil against terror and fight it the way Jatayu fought Ravana to try rescue Sita from the demon.
"Who was the first to stand against terrorism? Was he a warrior? Ramayana is witness that Jatayu was the first to fight against terrorism. He fought for a woman's honour," Modi said in his Vijayadashmi address at Lucknow's Aishbagh Ramleela ground.
Addressing a massive crowd, the Prime Minister said terrorism was one of the modern forms of Ravana - "the enemy of humanity".
"Ravana today has raised his head in a different form. If a country of 1.25 crore keeps an eye on every terrorist activity, terrorists will never succeed," he said, beginning and ending his speech with loud cries of "Jai Shri Ram, Jai Jai Shri Ram".
"We cannot become Ram but can all try and be Jatayu and fight terrorism," Modi said to loud cheers.
Communalism, casteism, nepotism are forms of evil inside us, need to get rid of these 'Ravanas', said PM.
He said after the 1993 Mumbai serial blasts, the US described terrorism as a law and order problem. "But after (2008 Mumbai attack) they came around and started talking about terrorism."
Modi said the fight against terrorism was not over. "If you think we are free from terrorism, then you are wrong. It is a virus affecting our society."
In a veiled reference to Pakistan, the Prime Minister said that countries which support terrorism should not be spared.
Prime Minister Narendra Modi stressed that the world needs to come together to fight terror and called upon Indians to unite and be vigilant against the menace.
"The world needs to come together against terror and destroy from the root those who spread terror and those who give shelter to terror," PM said.
Calling upon all Indians to be vigilant against terrorism, he said: "(If) we, one and a quarter billion Indians, come together and be vigilant against terrorists, terrorists cannot succeed."
Modi noted that some years ago, the world did not believe that India was suffering from terrorism.