Kenney made the resettlement of Iraqis a focus in 2009 and had initially set this year as the target date to resettle thousands fleeing persecution and violence in that country.
But the ongoing conflict in Syria forced the government to close its visa office in Damascus in 2012, which dramatically slowed down the Iraqi program.
Kenney says around 16,000 Iraqis have now arrived and the entire group will be resettled by 2015.
By 2018, they will be joined by some 5,000 Iranian and other Iraqi refugees currently in Turkey.
Focusing on targeted populations for resettlement is set to become the norm for Canada's refugee program, which is in the midst of a major overhaul.