* Mutual distrust has prevented withdrawal from border area
* Pulling out armies a condition for restarting oil flows
* Oil exports vital for Sudan and South Sudan
By Aaron Maasho and Hereward Holland
ADDIS ABABA/JUBA, Jan 17 (Reuters) - South Sudan started withdrawing its army on Thursday from the border with Sudan to set up a buffer zone, the government said, part of a peace deal that stipulated both must pull back troops before oil exports can restart.
The countries came close to war in April in the worst border clashes since South Sudan declared independence from Sudan in 2011 under an agreement which ended decades of war fuelled by ideology, oil, ethnicity and religion.
After mediation from the African Union, they agreed in September to resume oil exports from landlocked South Sudan through Sudan. Oil is vital to both economies.
"By withdrawing its forces ... the government of South Sudan is clearly demonstrating its full compliance with the signed security agreements and full commitment to their implementation," South Sudan's government said in a statement.
The pullout would be completed by Feb. 4 and South Sudan expected Sudan to do the same, the statement said.
Sudanese officials could not be reached for comment.
Mutual distrust remains deep and withdrawal from the disputed 2,000-km (1,200-mile) border was complicated by fighting on the Sudanese side between Sudan's army and rebels that Khartoum says South Sudan supports. Juba denies this.
Security officials from both countries are in talks in Addis Ababa to discuss implementing the buffer zone.
South Sudan, which says Sudan often bombs its territory, shut down its entire oil output of 350,000 barrels per day (bpd) a year ago after failing to agree export and transit fees with Khartoum. It had hoped to be producing 230,000 bpd by December.
Crude from southern fields will take two months to reach the Red Sea terminal on Sudan's coast after output resumes, South Sudan's oil minister said this month, suggesting exports could hit markets by April if the buffer zone is in place by February.