American national seized after armed men attacked his car near the city of Quetta.
The Pakistan military launched an operation against the groups operating in Swat in 2007.
Fazlullah’s supporters have blown up 173 schools, 105 of them for girls, since 2007, Sher Afzal, a Pakistani education ministry official, said last month.
‘Out of control’
Kamal Hyder, Al Jazeera’s correspondent in the Swat valley, said that decapitated bodies of policemen, left with notes warning authorities, were now a common sight on streets in the area.
“It is out of control, because the elected representatives of the people who were promising to bring peace … disappointed their people when they ran out of the area after their escalation of violence, leaving most of their supporters in the lurch,” he said.
“[The people] still need a political administration on the ground.”
Hundreds of people have reportedly fled the area in recent days, heading for two relief camps opened at schools in and near the region’s main city of Mingora.
“We are facing a very dangerous situation,” Wajid Ali Khan, a provincial minister, said.
“The fighting in the valley has made it almost impossible for civilians to stay there anymore.”
Up to one third of the 1.5 million population is estimated to have left Swat, which until recently was a prime tourist destination because of its natural beauty.
Speaking to Al Jazeera, Imtiaz Gul, a Pakistani security analyst, said what prevails in Swat “is a very difficult and complex situation” that will need both a military and political approach to resolve.
“It has to be a combination of blitzkrieg, surgical strikes and operations in the Swat valley, backed up by the civilian administration as well as the political leadership,” he said.
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“Most of the representatives have simply abandoned the area for fear of their lives … more than 70 per cent of policemen have either left their jobs, are sitting at home, or have been eliminated or executed.”
Yusuf Raza Gilani, Pakistan’s prime minister, pledged on Monday to restore peace to the Swat valley.
“We are finding a way out. We do not want to disclose the strategy right now, but soon Swat will be peaceful, like the rest of the country,” he said.
Gilani suggested that negotiations could end the violence, despite some security officials criticising a previous peace deal with pro-Taliban fighters for allowing them to regroup and strengthen.
“We are looking at various options. We have both the capacity and the will, but we want a strategy in which there is no collateral damage,” he said
“We are all concerned about the life and property of the people. We are also concerned about those who are migrating.”