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The ambush was carried out "by a terrorist group that infiltrated into Iraqi territory coming from Syria," the ministry said on its website.
It said a number of unarmed and wounded Syrian soldiers had fled to Iraq for medical treatment and were being transferred to Al-Walid border crossing to be returned to Syria through "official channels."
But they were ambushed on the way, in what the ministry termed "an attack against the sovereignty of Iraq, its land, and its dignity, and a clear violation of human rights, as (the soldiers) were wounded and unarmed."
The ministry also issued a warning to all sides in the Syria conflict "against moving their armed conflict to Iraqi territory and violating Iraq's borders."
Baghdad has pointedly avoided calling for the departure of Syrian President Bashar al-Assad, who is locked in a bloody civil war with rebels opposed to his regime, and has instead urged an end to violence by all parties.