Sherman says he is calling for federal intervention because a large number of the children who have died while in care were aboriginal.
He says the federal and provincial governments must work with First Nations leadership to fix the problem.
Human Services Minister Dave Hancock says Sherman is "grasping at straws."
He says Sherman's letter would serve a better purpose if it asked Prime Minister Stephen Harper for financial help instead.
Sherman says he sent the letter Wednesday night and he hasn't received a reply yet.
"Let's bring forward meaningful solutions," Sherman said Thursday. "There's no reason to lay blame on anyone and that's what inquiries are about, fixing the problem once and for all and restoring trust and confidence in the system."
Hancock acknowledged the federal government has a role with respect to First Nations.
"And we would like to engage them more fully in that role, but it's not in asking them to have some sort of public inquiry," he said. "They can play a meaningful role at the table with resources."
Hancock has promised a roundtable with opposition members and stakeholders to explore problems raised in stories by the Edmonton Journal and the Calgary Herald this week.
The newspapers said a lengthy investigation of records revealed the province has failed to publicly report the deaths of 89 foster children in the last 14 years.
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