In a letter dated March 9, a Canadian official demanded that HP repay that amount by March 22 or provide proof that goods and services worth $120 million were delivered at proper billing rates.
Canada claims that there is insufficient evidence that the charges were justified.
In a statement, HP said it "believes that there is no merit to the government's demands and intends to defend vigorously any claim, if brought."
Canada's repayment demand comes after internal audits and a police investigation into billing irregularities related to computer subcontractors. A civilian employee at the armed forces' headquarters was fired in September.
Canada has also demanded information from HP related to a total of $277 million billed to the Department of National Defence (DND) from 1991 to 2003. That figure includes the disputed $120 million.
HP suggested that the dispute stems from a defense department request for the company to process invoices for suppliers, whose work HP knew little about.
"DND's instructions to HP were to process invoices for these suppliers, although the nature of the work being performed was, in many instances, never disclosed by DND," HP said in a statement.
A representative for the Canadian defense department said his agency is not responding to that statement at this time.