Kenney was responding to concerns raised after a Saskatoon man, in need of drugs related to chemotherapy, discovered the federal government would not be footing the bill due to his status as a refugee claimant.
Saskatchewan, however, has since stepped in to cover the man's health care costs.
Kenney said Monday the province's move is fine by him.
"If they want to make exceptions, if they want to provide expansive health insurance for foreign nationals who are here, out of status or temporarily, they are welcome to do so," Kenney said Monday in the House of Commons. "We have no objection to that whatsoever."
Kenney noted that no one can be declared a refugee until they are deemed so after going through an application process.
Saskatchewan's Minister of Health, Dustin Duncan, said Monday that directives have been issued to health regions in the province to provide treatment for all urgent health needs of people going through the refugee process.
"We don't want health regions and our hospitals and acute care facilities to be turning people away, particularly those in emergent and urgent need of care," Duncan said.
Duncan added the province is still trying to change the federal government position on cuts to health benefits for refugee claimants and found Kenney's attitude unhelpful.
"That's unfortunate that that's the tone that the federal minister has taken," Duncan said 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."
Duncan noted it can months or years for a person seeking refugee status to learn his or her fate.
"To then leave that individual in limbo like this, that's discouraging to hear that," he said.
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 added he is writing Kenney because the changes have confused health officials.