Joseph Zikuski, the Binghampton police chief, said there were "14 confirmed dead
in the building" and that he had "very good reason to believe that the shooter is among the dead at the scene".
"We removed safely 37 people. Four people we removed are wounded. All four are listed in critical condition," Zikuski said.
Earlier reports had said that two men were led away from the scene in handcuffs although the authorities later said they were not considered suspects in the killings.
The man entered the building in Binghamton, about 240 km northwest of New York city, and immediately shot two receptionists, Zikuski said.
|Police say the attack was premeditated [Reuters]
"It obviously was premeditated,'' said Zikuski, noting the gunman blocked the rear exit with his car. "He made sure nobody could escape.''
One receptionist was killed, but another pretended to be dead, then crawled to a desk and called authorities, he said.
Zhanar Tokhtabayeva from Kazakhstan said she was in an English class when she heard a shot and her teacher screamed for everyone to hide in the storage room.
"I heard the shots, every shot. I heard no screams, just silence, shooting,'' she said.
"I was thinking, when will this stop? I was thinking that my life was finished.''
Pakistani Taliban claim
Baitullah Mehsud, the leader of the Pakistani Taliban, claimed in a phone call to Al Jazeera that he had ordered the shooting, saying a second attacker had managed to escape the immigration centre.
He said the attack was in direct response to the drone attacks carried out by US forces on Pakistani tribal areas.
Al Jazeera's Kamal Hyder, reporting from Pakistan, said that "if Baitullah Mehsud indeed is responsible, it could have serious consequences".
The American Civic Association is an organisation that helps immigrants in the Binghamton area with citizenship applications, according to US Citizenship and Immigration Services.
Shooting incidents have become increasingly common in the US, where guns are widely available and the rights to own them are fiercely debated.
In 2007 in one of the worst incidents, a student went on a gun rampage killing 32 people at Virginia Tech University, in Blacksburg, Virginia.