"We completely, absolutely reject the Awakening becoming a third military organisation," al-Obaidi said at a news conference.
He said the groups would also not be allowed to have any infrastructure, such as a headquarters building, that would give them long-term legitimacy.
Al-Obaidi said: "We absolutely reject that."
The Iraqi government has pledged to absorb about a quarter of the men into the security services and military, and provide vocational training so that the rest can find jobs.
Integration would also allow Sunnis to regain lost influence in the key defence and interior ministries.
The government has been vague about its plans and the interior ministry has agreed to hire about 7,000 men so far on temporary contracts, and plans to hire an additional 3,000.
But the ministry has neither specified the length of the contracts nor the positions the men would fill.
The Sunni irregulars have contributed to a 60 per cent drop in violence in the last half of the year.
The infusion of thousands of US troops and a six-month cease-fire by Muqtada al-Sadr, the Shia leader, are believed to be the other contributing factors.
Although there have been far fewer attacks, violence has by no means been eradicated.
A suicide car bomb exploded at a checkpoint manned by Iraqi army and police in the western Baghdad neighbourhood of Ghazaliya on Saturday afternoon, killing four people and wounding six, a police officer said.
On the southern outskirts of the capital, a roadside bomb injured five bystanders near a hospital in the town of Madin, police said.
To the north in Mosul, 360km northwest of Baghdad, another roadside bomb targeting a passing police patrol killed one policeman and injured two others, local police said.
In Diyala, US soldiers discovered a Shia village that had been systematically destroyed in an area where al-Qaeda in Iraq has been operating in recent months.