Malala Yousafzai, the Pakistani girl shot in an attempted assassination by the Taliban in October, has spoken publicly for the first time of her recovery in Britain, saying God has given her "a second life" thanks to the prayers of those who supported her around the world.

In a short video recorded in the days before her most recent operations on Saturday, Malala said: "Today you can see that I am alive. I can speak, I can see you, I can see everyone and … I am getting better day by day. It's just because of the prayers of people. Because all people – men, women, children – all of them have prayed for me.

"And because of these prayers God has given me this new life … and this is a second life. And I want to serve. I want to serve the people. I want every girl, every child, to be educated."

In another video recorded on Sunday, the day after her operations, Malala said she was happy that both operations had proved successful. She had been under anaesthetic for five hours. "I can also walk a little bit, I can talk and I am feeling better, and it did not seem I had a very big operation." She again spoke of her "mission" to help people.

Malala has been treated at the Queen Elizabeth hospital in Birmingham since being flown to Britain after being shot by the Taliban for campaigning for women's rights and girls' education. She underwent cranial reconstruction and a procedure for a cochlear implant in what doctors hope will be her last round of operations.

The neurosurgeon Anwen White said on Monday that she hoped the teenager would be discharged home "fairly soon".

Her father, Ziaddudin, has been appointed an education attache to Pakistan's consulate in Birmingham.

Malala, who also spoke in Urdu and Pashto in the first video, announced the creation of the Malala Fund with the help of a US-started non-governmental organisation. Alyse Nelson, the Vital Voices president and chief executive, said: "We stand with Malala and girls around the globe who are boldly speaking out as advocates for education and equality. When girls move forward, they take their communities forward too."

The fund will support the education and empowerment of girls in Pakistan and around the world and will provide grants to civil society organisations and individuals focused on education. It will be advised by a committee comprising education experts and entrepreneurs, as well as Malala and her family.

A statement on the fund's website said: "Before she was attacked, Malala was in the process of setting up an organisation with her friends to get girls into school and out of domestic labour. The first grant of the Malala fund will continue this process and provide a safe space for the girls, resources for a positive learning environment and an incentive programme for families. After a needs assessment and final programme design, the project will be launched and running by spring 2013."