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U.S. and Pakistani investigators are giving increased credence to links between Times Square bombing suspect Faisal Shahzad and the Pakistan Taliban, with one senior Pakistani official saying Shahzad received instruction from the Islamist group's suicide-bomb trainer.

If the links are verified, it would mark a stark shift in how the Pakistan Taliban—an affiliate of the Taliban in Afghanistan—and related jihadist groups in Pakistan pursue their goals. Until now, they have focused on attacks within Pakistan and in India, not the U.S.

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For the past several months, Pakistan's military has waged a battle against the Pakistan Taliban and a related group, Jaish-e-Mohammed, in the Pakistani tribal region of South Waziristan, which borders Afghanistan. The Pakistan Taliban's leadership has been heavily targeted by missile strikes from Central Intelligence Agency pilotless drones.

Pakistani investigators also are probing Shahzad's possible connections with Jaish-e-Muhammad, an outlawed Islamist militant group, after the arrest Tuesday of Tohaid Ahmed and Mohammed Rehan in Karachi. A senior Pakistani government official said the two men were believed to have links to Jaish. Ahmed had been in email contact with Shahzad; Rehan took Shahzad to South Waziristan, the official said.

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There, Shahzad received training in explosives in a camp run by Qari Hussain, the official said. Hussain is a senior commander with Tehrik-e-Taliban Pakistan, the Pakistan Taliban's formal name, and trains suicide bombers, the official said. Mr. Hussain is also a cousin of Hakimullah Mehsud, the Pakistan Taliban's chief. The 30-year-old Shahzad has admitted to investigators that he received training from militants in Waziristan, U.S. officials said.

After several trips to Pakistan, Shahzad came back to the U.S. with significant amounts of declared cash, law enforcement officials said. "That's not that unusual, for immigrants to move with lots of cash," he said. "There just wasn't anything in his [immigration file] that raised any red flags."

Hussain claimed responsibility for the attempted attack in a weekend audio message. His message followed a video of Mehsud, the Pakistan Taliban leader, in which he warned of a wave of attacks on the U.S. "Our fighters are already in the United States," Mehsud said.

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