"They thought that the bullet would silence us, but they failed," Malala said on her 16th birthday in a presentation in which she called for books and pens to be used as weapons.
"The terrorists thought that they would change my aims and stop my ambitions, but nothing changed in my life, except this: weakness, fear and hopelessness died. Strength, power and courage was born," she said. (Read: Highlights of Malala's speech at UN)
Her 20 minute speech was given several standing ovations and was quickly hailed for her message of peace.
Malala, who wore a pink headscarf and a shawl that belonged to assassinated Pakistan leader Benazir Bhutto, insisted she did not want "personal revenge" against the Taliban gunman who shot her on a bus in Pakistan's Swat Valley on October 12 last year.
"I want education for the sons and daughters of the Taliban and all the terrorists and extremists. I do not even hate the Talib who shot me. Even if there is a gun in my hand and he stands in front of me I would not shoot him."
But Malala said "the extremists were and they are afraid of books and pens, the power of education. The power of education silenced them. They are afraid of women."
"Let us pick up our books and pens. They are our most powerful weapons. One child, one teacher, one pen and one book can change the world. Education is the only solution," she said.
The passionate advocate for girls education was shot in the head by a Taliban gunman as she road on a school bus near her home in Pakistan's Swat Valley in October.
She was given life-saving treatment in Britain where she now lives, but the attack has given new life to her campaign for greater educational opportunities for girls.
Malala is now considered a leading contender for the Nobel Peace Prize. The Taliban have made it clear however that she remains a target.
Gordon Brown, the former British prime minister and UN special envoy for education, hailed Malala as "the bravest girl in the world" as he presented her at the UN Youth Assembly.
Brown said it was "a miracle" that Malala had recovered to be present at the meeting.
UN leader Ban Ki-moon and other top officials also hailed her achievements.
The speech in which Malala invoked the legacy of Martin Luther King, Nelson Mandela and other legendary peace advocates brought quick praise.
Malala also thanked British doctors and nurses for the care they had given and the United Arab Emirates government for paying for her treatment.
"I cannot believe how much love people have shown me. I have received thousands of good wish cards and gifts from all over the world. Thank you to all of them. Thank you to the children whose innocent words encouraged me," she said.
British Prime Minister David Cameron said on his twitter account that Malala had delivered a "powerful message".
The United Nations estimates that 57 million children of primary school age do not get an education -- half of them in countries at conflict like Syria.
"Students and teachers across our globe are intimidated and harassed, injured, raped, and even killed. Schools are burned, bombed, and destroyed," said Diya Nijhowne, director of the Global Coalition to Protect Education from Attack.
Nijhowne highlighted a horrific attack in northern Nigeria last week.
Gunmen from the Boko Haram Islamist group -- whose name literally means "Western education is a sin" -- broke into a secondary boarding school and killed 41 students and one teacher before setting fire to the building.
According to Ban's annual report on children and conflict, 115 schools were attacked last year in Mali, 321 in the occupied Palestinian territory, 167 in Afghanistan and 165 in Yemen.
Pakistan has an estimated five million children out of school and Nigeria 10 million, according to UN estimates.