Foreign Minister Hina Rabbani Khar has demanded Fazlullah?s extradition during her meeting with US special envoy to Pakistan and Afghanistan Mark Grossman.
Grossman was told that Fazlullah was involved in the attack and that the US should use its influence for his extradition, Geo TV reported on Monday.
Fazlullah and his associates have been hiding in Afghanistan?s Kunar province, and have carried out 15 cross-border attacks over the past one year, according to officials.
They also said that the gunman involved in Malala?s attack has fled to Afghanistan.
Fourteen-year-old Malala Yousafzai was shot in the head by a Taliban gunman in Khyber Pakhtunkhwa province October 9.
She was on her way home from school when an attacker wearing police uniform stopped the school bus and opened fire at her. She was seriously injured.
The Taliban said they attacked Malala, Pakistan?s first National Peace Award winner, for ?promoting secularism?.
She was flown to Britain for treatment and is undergoing treatment at the Queen Elizabeth Hospital in Birmingham.
Malala came to prominence in 2009 at the age of 11, when she started writing a diary for BBC Urdu about life under the Taliban.
Under the pen-name Gul Makai, she described the problems caused by militants who had taken control of the Swat Valley where she lived in 2007 and ordered girls? schools to close, according to the BBC.
Meanwhile, the Pakistani Taliban have threatened to attack another schoolgirl for exposing their atrocities, the Dawn reported on Monday.
Hina Khan from Swat was on the Taliban hit list for publicly criticising their atrocities, the daily said.
Her family has claimed that despite repeated requests for security from the authorities, no protection was provided to them. They relocated to Islamabad a few years ago.
?But now I feel I would not be able to go to school in Islamabad as well after the renewed threats,? Hina, a Class 11 student, told the newspaper.
?I am more worried now because after the attack on Malala, a red cross on our door and subsequent threats to my family, has made us more insecure,? she said.
According to her father Raitullah Khan: ?A few days ago when I came out of my house I saw a red cross on my gate but I removed it assuming it might have been drawn by some kids, but the very next day it appeared again, which really terrified me.?
?Next day, we received a call that Hina will be next after Malala,? the daily quoted Khan as saying.
The British hospital treating Malala has raised hopes for her recovery on Friday when doctors said she was able to stand with some help and to write.
Doctors had said she had shown signs of infection and faces a long, difficult recovery with uncertain prospects.
?She is not out of the woods yet,? hospital medical director Dr Dave Rosser had said then. ?Having said that, she?s doing very well. In fact, she was standing with some help for the first time this morning when I went in to see her.?
Malala has come to be a symbol for a girl?s right to education.
At the age of 11, she began writing a blog under a pseudonym for the BBC about life under the Taliban in the Swat Valley. After the military ousted the militants in 2009, she began publicly speaking out about the need for girls? education. She appeared frequently in the media and was given one of the country?s highest civilian honors for her bravery.