Sourin Roy, chief secretary of the West Bengal state government, told reporters the arrests were made Tuesday night on the outskirts of Basirhat, 40 miles north of the eastern city of Calcutta and close to the India-Bangladesh border.
He said the five Bangladeshi men were to appear in court later Wednesday.
"We are verifying their links with Pakistan's spy agency and a Dubai-based mafia don, but we can't disclose details at this stage," Roy said.
Calcutta police said they seized a motorcycle belonging to Korban Ali, one of the arrested religious teachers. They said the motorcycle may have been used in the attack on the American Center early Tuesday morning.
The assailants killed four Indian policemen and injured 20 other people, mostly policemen. Also injured were a passerby and a contract guard on duty at the American Center.
Police officers who survived the attack said their own guns Enfield bolt action rifles dating to World War I either jammed or were unloaded. They described the gunmen were professional and determined.
"How can you expect us to face these gunmen armed with AK-47s?" Bablu Mondal told The AP from his hospital bed Wednesday.
Indian officials have blamed the attack on Harkat-ul-Jehadi-al-Islami, a Pakistan-based group with a little known branch in Bangladesh. The group, founded by Fazlur Rahman Khalili, has been fighting since 1994 to merge India's portion of Kashmir with Pakistan.
Khalili is based in Lahore, Pakistan, R.S. Bhullar, the director-general of India's Border Security Force, said in Srinagar.
Harkat denied Tuesday any involvement in Tuesday's attack.
Around 200 Harkat militants are believed to have entered Kashmir since the United States began military strikes against Afghanistan in October, Bhullar said.
India accuses Pakistan's Inter-Services Intelligence spy agency of supporting the militants with arms and training, a charge that Pakistan denies.
In July 2000, Bangladesh's then-home minister, Mohammad Nasim, said the Harkat branch in Bangladesh had links with the Taliban rulers in Afghanistan, who are charged with supporting Osama bin Laden's al-Qaida network. Two years ago, police accused the Harkat of planting explosives in a soccer field before Bangladesh's then-Prime Minister Sheikh Hasina was to give a speech.
The new government, headed by Prime Minister Khaleda Zia, has said there is no Islamic radical group in Bangladesh linked to the Taliban.
Indian officials have also suggested a Dubai connection with the attack on the American Center. They say that telephone calls claiming responsibility came from the Gulf state, and that the attackers may be connected to the leader of a criminal gang taking refuge there.
India's hom minister, Lal Krishna Advani, said Tuesday the attack was an act of terrorism against U.S. and Indian interests. But U.S. State Department and FBI officials have said they have no evidence of that.
U.S. officials have said the attack appeared to target Indian policemen. It took place during a shift change, when more policemen were around, they said.
Asked if it was an attack against the United States, State Department spokesman Richard Boucher said Tuesday: "Until we know for sure who did it and why, I can't say one way or the other."
Mondal, the wounded policeman, said the attack by a person riding a motorbike and dressed in an olive military uniform was so sudden he hardly had time to react or retaliate.
"I saw only one motorbike and one person. I was fired at from an AK-47. The gunman seemed to be a thorough professional, trained in firearms as his hands never trembled while firing," said Mondal, who was shot in the hand.
He said he look around and found three policemen shot dead and one injured. The injured policeman later died.
"I could have perhaps fired back had my hand not been hit," he said.
The West Bengal state government said that videotapes of the shooting were being reviewed. The tapes came from a closed-circuit camera on the roof of the American Center.
The center reopened Wednesday but the bloodshed and heavily armed police commandoes in front of the building were expected to dissuade visitors.
"We're open for business," Rex Moser, director of the American Center, said in a telephone interview. "There are new sandbags and armed commandos out front. I assume that would dampen attendance."
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