Cheney had asked Pervez Musharraf, the Pakistan president, to do more to stop al-Qaeda from rebuilding safe havens in Pakistani tribal lands and step up efforts to thwart a spring offensive by the Taliban against Afghan and Nato troops.
The Pakistani security official said Akhund's arrest was the culmination of a planned operation and not a result of Cheney's visit.
Taliban sources, speaking on satellite telephones from undisclosed locations, said Akhund was caught at the home of one of his relatives at the Baluchistan provincial capital.
They said two other Taliban leaders had been arrested in Quetta this week, but a Pakistani security official could not confirm this.