(CNN) -- Faisal Shahzad, the suspect in the attempted bombing of Times Square, was heading for Pakistan -- where he was born -- when he was arrested late Monday night.
His family originally comes from a village near Peshawar in Pakistan.
Pakistan's western areas, along the border with Afghanistan, have been a haven for Islamist radicals for years, despite efforts to bring it under control.
Shahzad told the FBI he trained at a terrorism camp in the Waziristan region of Pakistan, a U.S. administration official told CNN. However, the official said investigators have nothing to corroborate his account.
It was not clear whether Shahzad was referring to North or South Waziristan.
Hours after authorities arrested Shahzad, security forces in Pakistan seized two or three people in a raid connected with the failed bombing, a Pakistani intelligence source said.
The Pakistan raid took place in a house in Karachi's Nazimabad district, where Shahzad was believed to have stayed during his last visit to the country.
Shahzad is a naturalized U.S. citizen.
Both U.S. and Pakistani officials warned against jumping to the conclusion that Islamists in Pakistan played a role in the attempted bombing.
"We are seeing cases of individuals who have links to a range of countries around the world who for whatever reason have become involved in extremist movements," State Department spokesman P.J. Crowley said Tuesday, before Shahzad's claim he trained in Pakistan.
"I would be very careful about making a broad-brush statement. We value our relationship with Pakistan. We value the fact that there are many Pakistanis who have come to this country, have links to Pakistan and have become citizens of this country. We are very proud of them," he said.
A top Pakistani government minister said Shahzad had traveled back and forth from Pakistan to the United States regularly, but also said he had visited the Middle East as well.
"Faisal Shahzad first went to the United States in 2003 on a student visa. He has been going back and forth between Pakistan and the United States many times since then," Pakistani Interior Minister Rehman Malik told CNN.
"Shahzad has been visiting Middle Eastern countries," he added, but would not elaborate where and when.
When asked if Shahzad had received training by militants in Pakistan -- before Shahzad's claim was revealed -- Malik said "We don't have such information at this point."
Pakistan's military last year launched offensives against militants in the west of the country -- along the border with Afghanistan -- to try to wrest back control of its territory.
The offensives forced many residents from their homes.
But the attacks on the Pakistani Taliban in the Swat Valley and South Waziristan were inconclusive, U.S. officials suggested late last year.
In Pakistan, al Qaeda and other militants persist in planning strikes against U.S. interests in the region, a U.S. counter-terrorism official said in December.
"They've suffered some major losses, but no one should think for a second that they're down and out for good. They remain intent on harming the United States and our allies, including Pakistan, so keeping up the pressure on them is critical. That's exactly what we're doing," the official said, referring to the militants.
The Pakistani Taliban are distinct from the Afghan Taliban, although they are aligned.
The United States plans to send tens of millions of dollars to Pakistan for roads and power plants -- some of it to the Swat Valley -- the Obama administration announced in March.
CNN's Reza Sayah, Samson Desta, Carol Cratty, Virginia Nicolaidis and Pam Benson contributed to this report.