A unit set up to trace dangerous foreign criminals has been closed by the Home Office, despite seven remaining at large.
Mr Reid's predecessor was doomed by the row
The Home Office endured a wave of criticism after it was revealed 1,000 foreign prisoners were not considered for deportation before release.
Of these, 74 were sex offenders or violent criminals, including rapists, killers and paedophiles.
Those not found may be dead or abroad, Home Secretary John Reid said.
Police officers had recommended that the unit be closed down rather than it being a political decision, Mr Reid said. Other efforts to ascertain the fate of the remaining criminals would continue.
"We have got the vast majority of them now under lock and key," he told ITV1's The Sunday Edition.
"Some of them, we think, may be dead or out of the country. I think there are about seven of them that we haven't managed to locate.
"We believe some of those seven may have left the country or may not still be alive. The resources that we put into tracing the others - about 40 or 50 of them - have now come to the end of their useful life in their present configuration."
He vehemently denied any suggestion that the efforts to find the criminals had fallen short in any way.
"I think most people recognise that we can put enormous efforts into this, but it isn't possible always to accomplish 100% of everything. I'm the home secretary, not the Wizard of Oz."