Town officials said suspect Jiverly Wong had recently lost his job
US police are piecing together details of the man they say shot dead 13 people and took several hostages at a New York state immigration centre.
The man, who also killed himself, was identified as Vietnamese immigrant Jiverly Wong, 41. He used the alias Jiverly Voong, police said.
He reportedly lost his job recently and was frustrated by language problems.
Police said autopsies were under way on those who died but did not suggest a motive for the attack in Binghamton.
Earlier, Pakistani Taleban leader Baitullah Mehsud called media organisations including the BBC in Islamabad to claim responsibility for the attack.
But FBI spokesman Richard Kolko said that based on the evidence the militant's claim could be "firmly discounted".
In Friday's attack, the gunman apparently parked his car against the back door of the American Civic Association (ACA) buildings in the town of Binghamton, north-west of New York City.
The Associated Press reported that he walked into the building and opened fire, apparently without saying a word.
Detectives have searched Wong's home and removed items including computer hard drives and a rifle bag.
Two handguns used in the attack were registered under the name of Jiverly Wong, AP reported.
Town Mayor Matthew Ryan told ABC news that Wong had lost a job recently "and was somewhat angry".
"He had language issues, didn't speak English that well, and was really concerned about his employment situation."
The victims appear mainly to have been immigrants, taking English-language classes at the centre and receiving advice on settling in the US.
The authorities have been taking calls from worried relatives from all over the world.
'Most tragic day'
Zhanar Tokhtabayeva, a 30-year-old from Kazakhstan, was in an English lesson when her teacher screamed for everyone to go to the storage room.
WEEK OF SHOOTINGS
Sat 4 April: Gunman kills three policemen in Pittsburgh before being wounded and captured
Fri 3 April: Gunman kills 13 people at an immigration centre in Binghamton, New York state, then apparently shoots himself
Sun 29 March: Gunman kills seven elderly residents and a nurse at a nursing home in Carthage, North Carolina, then is shot and wounded himself
Sun 29 March: Man kills five relatives and himself in Santa Clara, California
"I heard the shots, every shot. I heard no screams, just silence, shooting," she told AP.
"I heard shooting, very long time, and I was thinking, when will this stop? I was thinking that my life was finished."
About 40 people escaped from the building - 26 of whom are believed to have hidden in the basement.
Four were critically injured in the shooting, north-west of New York City, police said.
Police Chief Joseph Zikuski told NBC TV channel how one of the centre's receptionists played dead after being shot in the stomach, and managed to call the emergency services.
He said the injured woman stayed on the telephone for 90 minutes, feeding the authorities information.
"She's a hero in her own right," he said.
Correspondents said Binghamton residents were struggling to come to terms with the tragedy.
Local newspaper the Press Sun & Bulletin reported that there had been just one murder in the town since the start of 2008.
Mayor Ryan called it "the most tragic day" in Binghamton's history.
President Barack Obama, in Europe for a Nato summit, said he was "heartbroken" for the families of victims of the "senseless tragedy".
Mr Obama said his administration was "actively monitoring the situation" and that Vice-President Joe Biden was in touch with officials in Binghamton.