"The ministry does not have any DNA test (results) for any relative of Duri at the present time," ministry spokesman Dr Ziyad Tareq told AFP.
Tareq said such results are necessary if DNA testing is to be able to positively identify a man killed a week ago by pro-government forces as Duri.
For years, Duri has been the most senior member of Saddam's regime still at large.
Killing him would be a major victory for Baghdad, but Duri has previously been reported dead or captured only to resurface in subsequent audio or video messages.
The group's spokesman, Jaafar Husseini, told AFP that two men captured by Ketaeb Hezbollah who had seen Duri in the past six months said the dead man was him, but that account could not be independently confirmed.
Husseini said the man was killed near the town of Al-Alam north of Baghdad and his body was later transferred to the paramilitary group.
That squared with an account from Omar Abdullah al-Jbara, a leader in the local forces from Al-Alam, who said volunteers and police clashed with a group of men on April 17, killing 12, including one who resembled Duri.
But little has been heard from JRTN and other groups since, with the Islamic State jihadist group, which led the drive, dominating the conquered territory.
Senior members of Saddam's Baath party, to which Duri belonged, have also reportedly played a major role in IS itself.
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