But Khan said that when officers seized the pistol, the sword, a dagger and night-vision equipment (from Faulkner), their "suspicion grew".
Khan said Faulkner told police he was hunting bin Laden, who is accused of orchestrating the attacks on the World Trade Center in New York on September 11, 2001 that claimed almost 3,000 lives, because he had suffered personal losses in the attacks.
He added the alleged assailant was also carrying a book containing Christian verses and teachings.
When asked why he thought he had a chance of tracing bin Laden, Faulkner replied, "God is with me, and I am confident I will be successful in killing him," Khan said.
If confirmed, Faulkner's attempt to kill bin Laden would mark one of the first instances of an American entering Pakistan and Afghanistan on a solo mission to fight against al-Qaeda.
Faulkner had arrived in Chitral almost two weeks ago for his eighth visit to Pakistan.
He worked as a police guard, which is quite common for foreigners visiting remote parts of Pakistan.
But when he checked out without informing police, officers began hunting for him, Khan said.
Some Western governments believe bin Laden may be hiding in mountains along the Afghanistan-Pakistan border.
Washington has offered a bounty of $25m for information leading to the capture of al-Qaeda's head.
Richard Snelsire, the US embassy spokesman in Islamabad, said the Peshawar consulate had been informed of the arrest of a US citizen and added the embassy was seeking access to the detained American.