(CNN) -- Pakistani teenager Malala Yousafzai's inspiring speech at the United Nations on every child's right to go to school is just the beginning of a major push on education, former UK Prime Minister Gordon Brown said Saturday.
Yousafzai -- who on Friday gave her first public remarks since she was shot by the Taliban last year for advocating that all girls should go to school -- will return to the United Nations in September to press her point, according to a statement from Brown's A World at School campaign.
Accompanied by Brown, she will address an education summit of world leaders during the week of the full General Assembly at U.N. headquarters in New York, it said.
There, the 16-year-old will demand action on behalf of 57 million children around the world who have no access to any schooling.
Meanwhile, Brown, who's the U.N. special envoy for global education, will travel to Pakistan in July to discuss education issues with the country's new government. He also intends to visit Nigeria, Africa's most populous nation, in the fall.
Between them, Pakistan and Nigeria have 16 million children out of school, the statement said, most of them girls.
Brown and Yousafzai met with the United Nations' Pakistan high commissioner on Friday to discuss the plight of more than 5 million children who are out of school in the country, the statement said.
"Malala's speech was just the start of a momentous push for change in the run up to 2015, to deal with the education emergency," Brown said.
The Millennium Development Goal on education set by U.N. member states in 2000 pledged to have every child in school by 2015.
In her speech Friday, Yousafzai said the masked gunmen who shot her in the head in October, who also injured two other girls, had not silenced her ambitions but rather made her stronger.
"They thought that the bullets would silence us, but they failed," she said. "And then, out of that silence came thousands of voices."
She said that she doesn't seek revenge against the Taliban, who have threatened to hunt her down again and end her life, and that she's against no one.
"I am here to speak up for the right of education of every child," she said. "I want education for the sons and the daughters of all the extremists, especially the Taliban."
She also reflected on the very real dangers faced by teachers and students in Pakistan.
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 a girls' 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 a girls' campus in Quetta. Fourteen students were killed.
The speech, given on her 16th birthday, was not about her, Yousafzai added, but rather to give a voice to all the voiceless millions around the world fighting for their rights.
"Let us wage a global struggle against illiteracy, poverty and terrorism, and let us pick up our books and pens. They are our most powerful weapons," she said.
"One child, one teacher, one pen and one book can change the world. Education is the only solution. Education first."
CNN's Ashley Fantz, Saskya Vandoorne and Saima Mohsin contributed to this report.