More than 100 children were taken from their families in Northern Ireland by Catholic agencies to former British colonies, Health Minister Michael McGimpsey said.
Last month Prime Minister Gordon Brown expressed regret for the "misguided" Child Migrant Programme, telling the House of Commons he was "truly sorry".
He also announced a £6m fund to reunite families that were torn apart.
A total of 103 children were taken to countries such as Australia and Canada from Northern Ireland between 1938 and 1956.
Mr McGimpsey said: "It is actually tracking down the migrant children and their families and trying to make the connection.
"When I start to look at the issue I would have thought £6m would have been quite a stretch to make it do the kind of numbers we are really talking about."
He was asked about the matter during minister's questions at the Assembly. SDLP MLA Mark Durkan raised the issue.
The scheme sent poor children for a "better life" to countries such as Canada and Australia from the 1920s to 1960s, but many were abused and lied to.
More than 130,000 children, aged between three and 14, were sent to Commonwealth countries.
As they were shipped out of Britain, many were wrongly told their parents were dead, while parents were given very little information about where their children were going.
The former child migrants have told how on arrival they were separated from their siblings, and put into foster homes, state-run orphanages and religious institutions. Others were educated only for farm work.
Many were subjected to brutal physical and sexual abuse by those who were meant to be caring for them.
© Press Association