The U.N. had declared July 12 her 16th birthday "Malala Day." But she insisted it was "the day of every woman, every boy and every girl who have raised their voice for their rights."
The Taliban, which has long opposed educating girls in Pakistan as well as neighboring Afghanistan, said it targeted Malala because she was campaigning for girls to go to school and promoted "Western thinking."
In what some observers saw as another sign of defiance, Malala said the white shawl she was wearing belonged to Pakistan's first woman prime minister, Benazir Bhutto, who was assassinated in December 2007 when she returned to run in elections.
Malala recalled the Oct. 9 day when she was shot on the left side of her forehead, and her friends were shot as well. She insisted she was just one of thousands of victims of the Taliban.
"They thought that the bullets would silence us," she said. "But they failed. And then, out of that silence came thousands of voices. The terrorists thought that they would change our aims and stop our ambitions but nothing changed in my life except this: Weakness, fear and hopelessness died. Strength, power and courage was born."
Malala began her speech with a traditional Muslim prayer and later accused terrorists of "misusing the name of Islam and Pashtun society for their own personal benefits." She wore a traditional pink patterned South Asian dress and pants called a shalwar kameez and a matching head scarf.
Malala said she learned to "be peaceful and love everyone" from Indian independence leader Mohandas Gandhi and other global advocates of non-violence; from the compassion of religious figures Mohammad, Jesus Christ and Buddha; from the legacy of Martin Luther King, Nelson Mandela and Muhammad Ali Jinnah, who led Pakistan to independence in 1947.
"I'm not against anyone, neither am I here to speak in terms of personal revenge against the Taliban, or any other terrorist group," she said. "I'm here to speak about the right of education for every child."
"I want education for the sons and daughters of all 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 hands and he stands in front of me. I would not shoot him," she said.
Malala said her main focus was on the education of girls and the rights of women "because they are suffering the most."
"We cannot succeed when half of us are held back," she said, urging all communities to be tolerant and reject prejudice based on caste, creed, sect, religion or gender.
A report by UNESCO and Save the Children issued just before Malala's speech said 57 million youngsters were out of school in 2011, down from 60 million in 2008. But it said the number living in conflict zones rose to 28.5 million in 2011 and more than half were girls.
Malala said extremists kill students, especially girls, and destroy schools because they are afraid of the power of education and the power of women, "and they are afraid of change, afraid of the equality that we will bring into our society."
She also decried the fact that wars, child labor and child marriage are preventing boys, and especially girls, from going to school.
Malala received several standing ovations and everyone joined in a rousing rendition of "Happy Birthday." In U.N. corridors, her speech got rave reviews with some diplomats and observers predicting a future political career.
Former British prime minister Gordon Brown, the U.N. special envoy for global education who helped organize the assembly, called Malala "the most courageous girl in the world." She was airlifted to Britain for treatment and returned to school in Birmingham, where her family now lives, in March.
He said she was doing exactly what the Taliban didn't want her to do, and announced that 4 million people had signed an online petition calling for education for everyone.
One of the main U.N. goals set by world leaders at a summit in 2000 is to ensure that every child in the world gets a primary education by the end of 2015.
U.N. Secretary-General Ban Ki-moon urged stepped-up efforts to get 57 million youngsters into school in the next 900 days. He said it won't be easy given the first decline in international aid for basic education in a decade and recent attacks on students and schools in Nigeria, Pakistan and elsewhere.
"No child should have to die for going to school," Ban said. "Nowhere should teachers fear to teach or children fear to learn. Together, we can change this picture. ... And together let us follow the lead of this brave young girl, Malala. Let us put education first."