 Irqittuq was elected in the 1999 Nunavut general election.He won the electoral district of Amittuq in a close race defeating former Northwest Territories MLA Mark Evaloarjuk and three other candidates winning 33% of the popular vote.He ran for a second term in office in the 2004 Nunavut general election but was badly defeated by candidate Louis Tapardjuk finishing second last in a field of five candidates.