The Labour Minister, Alison Magaya, said that the LRA - Ugandan rebels operating from southern Sudan - had committed untold atrocities and had to be dealt with.
The minister, who is a retired general, said the army would launch its own operations to eradicate the LRA, separate from a current Ugandan offensive, which he said was limited to a mountainous area.
The move followed claims by the Sudanese Government that about 4,000 people have been displaced in southern Sudan by heavy fighting there between Ugandan troops and the LRA.
The refugees "are in urgent need of help", Sudanese Labour Minister Alison Manani Magaya said.
In March, Sudan allowed Ugandan troops to enter Sudan in pursuit of the LRA, which is accused of kidnapping thousands of children and forcing them to fight or serve as sex slaves.
A BBC correspondent in Khartoum says that the presence of the Ugandan forces is also causing disquiet in some circles, with one MP accusing the government of surrendering Sudan's sovereignty.
Child soldiers
Last week officials from the Roman Catholic Church in Sudan said hundreds of civilians had been killed by LRA guerrillas fleeing from Operation Iron Fist - as the Ugandan offensive is called.
The Church said the LRA insurgents raped and abducted girls and women, and burnt down six villages.
Another 500 people were forced to flee the area to escape the violence.
The rebels' aim is to overthrow the Ugandan Government and rule according to the Bible's Ten Commandments.
Hundreds of thousands of people have been displaced and at least 12,000 children abducted by the LRA for use as slaves, wives or fighters.
'Heavy handed'
The LRA used to receive support from the Sudanese Government, but relations between Khartoum and Kampala have eased over the last two years.
Uganda and Sudan signed an agreement in March allowing Ugandan troops to carry out search-and-destroy operations against the rebels, who launch cross-border raids from rear bases in southern Sudan.
But human rights groups have criticised Uganda saying that Operation Iron Fist is too heavy handed.
It is feared that if it comes to a shootout in the remote mountains many innocent children will be killed alongside LRA leader Joseph Kony.
The Ugandan army says casualties are inevitable but from their point of view once a child has been abducted, been given military training, and is pointing a gun at you, it becomes a legitimate target.