Story highlights Malala Yousafzai: After the bullets, "out of that silence came thousands of voices"

She addresses the U.N. Youth Assembly, a gathering of more than 500 youth leaders

"I don't even hate the Talib who shot me," she said Friday, her 16th birthday

"This is what my soul is telling me," she said. "Be peaceful and love everyone"

A Pakistani teenager nearly killed by Taliban gunmen for advocating that all girls should have the right to go to school gave her first formal public remarks Friday at the United Nations. It also happened to be Malala Yousafzai's 16th birthday.

"Today, it is an honor for me to be speaking again after a long time," she said. "Being here with such honorable people is a great moment in my life."

She looked out at an audience of hundreds of children from around the world and U.N. members, including Secretary-General Ban Ki-moon, and told them that she was wearing a pink shawl that once belonged to Benazir Bhutto , the two-time prime minister of Pakistan who was killed in 2007 in a suicide attack at a political rally.

"I don't know where to begin my speech," she said. "I don't know what people would be expecting me to say. But first of all, thank you to God for whom we all are equal and thank you to every person who has prayed for my fast recovery and a new life. I cannot believe how much love people have shown me."

JUST WATCHED Malala: I am one girl among many Replay More Videos ... MUST WATCH Malala: I am one girl among many 16:54

JUST WATCHED Malala asks women to fight for rights Replay More Videos ... MUST WATCH Malala asks women to fight for rights 01:20

JUST WATCHED The story of Malala Yousafzai Replay More Videos ... MUST WATCH The story of Malala Yousafzai 02:21

She went on to give a rousing speech, saying that she held no contempt in her heart for the masked gunmen who, on October 9, 2012, jumped on her school bus and shouted her name, scaring other girls into identifying her. The gunmen shot and injured two other girls as well as Yousafzai.

"They thought that the bullets would silence us, but they failed," she said. "And then, out of that silence, came thousands of voices."

Yousafzai said she doesn't want revenge against the Taliban, who have threatened to hunt her down again and end her life.

"Dear sisters and brothers, I am not against anyone," she said. "Neither am I here to speak in terms of personal revenge against the Taliban or any other terrorist group. I am here to speak up for the right of education of every child. I want education for the sons and the daughters of all the extremists, especially the Taliban.

"I don't 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."

That is the legacy of nonviolence she has been taught, she said, naming, among others, Martin Luther King Jr., Jesus Christ, Nelson Mandela and Mother Teresa.

"This is the forgiveness that I have learned from my father and from my mother," Yousafzai said. "This is what my soul is telling me. Be peaceful and love everyone."

Yousafzai took up the mantle of defending equal access to education when she was 11. She and her family were living in Pakistan's Swat Valley, where the Taliban had issued an edict in 2009 banning all girls from school. Writing anonymously in a blog for the BBC at the time, she praised her father for continuing to operate a school that defied that order.

JUST WATCHED Secret school attendee speaks to CNN Replay More Videos ... MUST WATCH Secret school attendee speaks to CNN 04:18

JUST WATCHED Girls defy the Taliban in Pakistan Replay More Videos ... MUST WATCH Girls defy the Taliban in Pakistan 03:43

She wrote of the constant, terrifying reminder that war lurked outside her door, and that her books offered peace.

"The night was filled with the noise of artillery fire and I woke up three times," she blogged. "But since there was no school I got up later at 10 a.m. Afterwards, my friend came over and we discussed our homework."

Her blog attracted the attention of media everywhere, particularly journalists in the West. For years, this small girl with a big voice made it clear that she wasn't going to be intimidated. In interviews, she spoke without her face covered.

"I have the right of education," she said in a 2011 interview with CNN . "I have the right to play. I have the right to sing. I have the right to talk. I have the right to go to market. I have the right to speak up."

Her speech Friday had that same, if not stronger, tone of determination.

"The terrorists thought that they would change our aims and stop our ambitions," she said, "but nothing changed in my life except this: Weakness, fear and hopelessness died. Strength, power and courage was born."

Speaking for children across the world, she told world leaders: "We are really tired of these wars."

Yousafzai went on to address specific attacks in Pakistan on teachers and schoolchildren. Earlier this summer, a teacher was gunned down in front of her son as she drove into her all-girl school. A school principal was killed and his students severely injured when a bomb was tossed onto a school playground at an all-girl school in Karachi in March.

In January, five teachers were killed near the town of Swabi in the volatile northern Khyber Pakhtunkhwa province, the United Nations says.

And, in June, a suicide bomber blew up a bus carrying 40 schoolgirls as it made its way to an all-girl campus in Quetta. Fourteen female students were killed.

"Dear sisters and brothers," she said, "we realize the importance of light when we see darkness. We realize the importance of our voice when we are silenced. In the same way when we were in Swat, we realized the importance of pens and books when we saw the guns.

"The extremists were and they are afraid of books and pens," she said.

"The power of education frightens them. They are afraid of women. The power of the voice of women frightens them."

This fear is partly based on the Taliban's own lack of education, Yousafzai said. And, she said, world leaders should "change their strategic policies" to press for peace and ensure that children's and women's rights are protected.

"We call upon all governments to ensure free, compulsory education -- all around the world for every child."

Yousafzai presented Ban, the U.N. secretary-general, with a petition signed by nearly 4 million people in support of the 57 million girls and boys around the world who are denied education.

In October, six men were arrested in connection with the attack on Malala and the other schoolchildren who were on the bus as they headed home from school.

All of the men were released from jail because of a lack of evidence against them. The one named as the primary suspect, identified by police as Atta Ullah Khan, a 23-year-old man from the Swat district, remains on the run, authorities told CNN.

Khan was studying for a master's degree in chemistry.