News reports this week quoted Rankin Inlet Deputy Mayor Sam Tutanuak as saying high grocery prices have forced dozens of the community's residents to scavenge for food at the local landfill.
In a later interview with APTN News, Tutanuak said Aglukkaq's office called the community's senior administrative officer asking for a written apology for the remarks.
In a written statement Friday, Aglukkaq, who is also the MP for Nunavut, said she is considering taking legal action against Tutanuak.
"The deputy mayor’s claims about this conversation are completely false. I am currently reviewing all of my legal options," Aglukkaq said on Friday.
"I was troubled when I heard recent reports about families in Rankin Inlet struggling to find food, so I followed up with my constituents to address these concerns.
"I also contacted the senior administrative officer in Rankin Inlet to learn more about these concerning reports. At no time, did I speak with the deputy mayor during this phone-call conversation. And at no time, did I or my office request an apology from anyone at the hamlet," Aglukkaq said in a written statement on Friday.
The opposition parties pressed the government for answers again on Friday, but Aglukkaq was in Calgary for an infrastructure announcement.
Aglukkaq's parliamentary secretary Colin Carrie told the House of Commons the minister never requested such an apology. He said the minister was simply seeking information so she could better serve her constituents.
Tutanuak could not immediately be reached for comment.