"We have 12 patients in Sulaimaniya that have lung infections that we suspect may be the bird flu virus," Kurdistan's deputy prime minister, Imad Ahmed, told Reuters, referring to one of the region's largest cities.
The most serious was 54-year-old Mariam Qader, who came from the same village as the dead girl and is believed to be a distant relative of the victim.
The village is close to Iraq's border with Turkey, where four children died from bird flu in recent weeks.
"Until now we have culled more than 400,000 birds," Kurdistan's health minister, Mohammed Khashnow, told Reuters, adding that teams were concentrating on a swathe of territory between Sulaimaniya and the Turkish border to the north.