Authorities offered no details regarding their release, and did not give any clue as to which group was behind the mass abduction in Iraq's Muthana province, some 370 kilometres southeast of the capital, Baghdad.
"Efforts are still ongoing to free the rest of the 26 kidnapped," the Foreign Ministry statement said, adding that it expressed "Qatar's hope that these efforts will be crowned with success."
Qatari government officials declined to elaborate. Iraq's Interior Ministry did not immediately respond to a request for comment.
Hunters from Gulf states, mainly Qatar, visit Iraq's vast western and southern desert areas for hunting and purchasing falcons.
Also Read
Iraqi authorities approve the expeditions and offer local police officers as guards, though the Iraqi Interior Ministry previously accused the hunters of not following their instructions and going into unsecured areas.
While Iraq and a US-led coalition battle the Islamic State group in other parts of the country, the predominantly Shiite province of Muthana remains under the control of the nation's central government.
Kidnappings for ransom also plague Iraq and the hunters may have proven a tempting target because they come from oil-and-gas-rich Qatar.