The decision comes ahead of highly anticipated talks aimed at quelling the contentious north-south border issues.
The decision to pull the military out of Abyei comes as Sudanese officials are scheduled to meet with their South Sudanese counterparts Tuesday in the Ethiopian capital, Addis Ababa.
The talks follow an escalation in fighting between the two sides last month.
Sudanese military spokesman Col. Sawarme Khalid Saad told reporters that the redeployment would help talks with South Sudan.
In a statement issued late Monday, Saad also denied reports that Sudan's army had attacked the disputed north-south border earlier that day.
"We have nothing to do with what happens in the South," Saad said. "The army has not crossed the international frontiers."
South Sudan military spokesman Col. Philip Aguer said Monday the country's Western Bahr-el-Ghazal, Northern Bahr-el-Ghazal and Unity states experienced three days of bombardment by Sudan.
The two countries are set to resume bitter negotiations on issues left over from the 2005 peace deal that eventually saw South Sudan break away from Sudan to form an independent nation in July last year after more than two decades of civil war. Among the most contentious issues are the separation of their once-unified oil industry and the demarcation of the long and ill-defined border.
The negotiations are led by former South African President Thabo Mbeki, who has been unable to push the two sides closer to a deal.
Sudan's planned withdrawal of troops would be followed by the creation of a police force and parliament for the territory, Khartoum's official in charge of Abyei affairs Al-Khair al-Faheem Mekki told state Radio Omdurman.
The U.N. Security Council this month extended its security force's mission in Abyei, which includes about 4,000 peacekeepers, and demanded that Sudan withdraw their troops from the region following South Sudan's removal of about 700 police officers in early May.
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(Photo: REUTERS/Mohamed Nureldin Abdallah)