Kenney said provinces can offer more health coverage for refugee claimants if they want to, but Ottawa will not.
"We provide the same package of basic hospital and physician services that are typically available to Canadians," Kenney told the House of Commons on Monday.
"Not every province funds all of the same services precisely the same way. However, if provinces want to provide additional insurance for certain services to asylum claimants, they are more than free to do so."
The issue has come to the forefront because Ottawa denied chemotherapy to a refugee claimant in Saskatoon.
Duncan was not pleased with Kenney's stance.
"That's unfortunate that that's the tone that the federal minister has taken," he told reporters in Regina.
"It's the federal government, not the provincial government, that runs the refugee system and so we have no way to dictate or determine how long that process takes."
"For an individual to live in this province for what can be many months, if not years, waiting for a decision on the federal government and the court system of whether or not they'll be allowed to stay in this province, to then leave that individual in limbo like this, that's discouraging to hear that."
The man arrived in Saskatoon several months ago after fleeing a Middle Eastern country where he was persecuted for being Christian. Soon after arriving, he started having abdominal pain and was diagnosed with cancer.
Ottawa announced changes in the spring to the Interim Federal Health Program, which provides temporary health coverage for protected persons, refugee claimants and other groups not eligible for provincial health insurance.
Under those changes, some refugee claimants saw cuts to their drug, dental and vision coverage. Additionally, those whose refugee claims are rejected and those from a yet-to-be defined list of "safe'' countries will only receive medical care if their condition is deemed a risk to public health or safety.
The federal government said it hopes the changes will deter bogus refugee claims and ensure failed asylum seekers don't take advantage of Canada's free health care.
Duncan said he is writing Kenney because the changes have confused provinces and health officials.
He also said a review of the overall policy "would be in order."
"The changes that the federal government announced earlier this year lack clarity and that even by their own guidelines of urgent and essential nature, that this would clearly meet that test," he said.
Saskatchewan has picked up the tab for the man's chemotherapy.