Hancock has invited the three opposition parties to form a roundtable to study whether enough is being done to investigate and publicly report on foster-care deaths.
He says the group would write a report that would be delivered to the legislature.
But opposition leaders continue to call for a public inquiry.
They say the issue is too important not to be examined thoroughly and independently.
Premier Alison Redford has said that since she became premier in 2011 her government has taken steps to ensure all foster-child deaths are properly reported and investigated.
The Edmonton Journal and the Calgary Herald newspapers reported Monday that the province made public 56 of 145 deaths of children in care in the last 14 years.