Al-Zayadi said: "An armed group driving dozens of pickup trucks kidnapped at least 26 Qatari hunters from their camp in the area of Busaya in the Samawah desert near the Saudi border."
No group has yet claimed responsibility for the abduction but Iraq's Interior Ministry said they aimed "to achieve political and media goals".
Two Iraqi intelligence officers tasked with protecting the party were also taken, but later released.
Qatar's foreign ministry has asked Iraq for "details about the kidnapping" and urged them "to work to release them as quickly as possible".
The hunters entered Iraq with an "official permit' from the interior ministry, it added in a statement released to the QNA news agency.
Wealthy citizens from Sunni Gulf states are known to travel to Middle Eastern nations including Pakistan, Afghanistan and Iraq to hunt falcons.
There, the hunters are not restricted to the same quotas and conservation measures as they would be at home.
There is a degree of hostility towards over Gulf nations in Iraq's Shi'ite majority south, where some believe they were complicit in the rise of ISIS. No connection has ever been proven.
Qatar, which has financially backed rebels fighting to overthrow Syrian President Bashar al-Assad, is especially reviled there because local Iraqi factions have sent fighters to prop up his regime.
The abductions come just three months after gunmen took 18 Turkish citizens in Baghdad, before releasing them unharmed.
Turkey, like Qatar, has close ties to Syrian rebel groups and is accused by some of not doing enough to combat Isis.
Two of them were released in the southern province of Basra and the other 16 on the road to Karbala, also south of Baghdad.
Iraqi security forces clashed with fighters from the powerful Ketaeb Hezbollah militia during the search for the kidnapped Turks.
- Daily Mail
