The Times said US immigration officials had identified about 300 immigrants believed to have concealed their involvement in wartime atrocities, but the number could eventually top 600.
The accused immigrants included a soccer coach in Virginia, a metal worker in Ohio and four hotel casino workers in Las Vegas.
Immigration officials have uncovered evidence that as many as 150 of the Bosnian suspects took part in the 1995 Srebrenica massacre in which about 8000 Muslim boys and men were killed.
More than 100,000 people were killed in the 1992-95 Bosnian war which followed the break up of the former Yugoslavia.
"As long as we are alive, war criminals will never be in peace. The fact that investigators will come knock on their door one day is a start," Ms Subasic said.
The over 120,000 Bosnian refugees who started asking for American visas in the mid-1990s were required to disclose military service or links that would hint at involvement in war crimes.
However, the system counted on applicants being honest and only a minor effort was made to check out their stories.
Asked about it at his post cabinet press conference, Mr Key said he was not aware of any information to support the claim in reference to New Zealand.
He said the Refuge Council would be concerned about it "but I don't think there is a lot of validity to it."
"I'm sure someone will look into it."
The Refugee Council of New Zealand said it was highly unlikely any Bosnian war criminals were living in the country.
"The Refugee Council would be sceptical that what she's [Ms Subasic] saying is in fact true, but at the same time we have to have an open mind," council spokesman Gary Poole said.
Any evidence Ms Subasic had, including names and identities, should be immediately forwarded to the New Zealand Government, he said.
Tough screening processes as well as the type of Bosnian refugees who settled in New Zealand during the 90s meant it was "highly unlikely" war criminals were accepted into the country.
Between 400 and 500 Bosnians settled in New Zealand from 1993 - 1995, and about 600 arrived from 1997 and 1998, he said.
The majority of these people were women and children classed as "high protection cases", Mr Poole said.
"It is highly unlikely that there would be any war criminals among the women and children.
In addition to rigorous checks made by Immigration New Zealand, refugees also passed a screening process by the United Nations, Mr Poole said.