JUBA (Reuters) - South Sudan's President Salva Kiir is willing to meet his Sudanese counterpart Omar Hassan al-Bashir to sort out conflicts and resume vital oil flows, a South Sudanese minister said on Friday after Bashir agreed to hold a summit.

The neighbors agreed in September to set up a demilitarized border zone and resume oil exports from landlocked South Sudan through Sudan. Oil is the lifeline of both economies.

Neither country has yet withdrawn its army from either side of the border, a precondition to resume oil flows. Both sides accuse each other of supporting rebels on the other's territory.

South Sudan initially had planned to resume exports by year-end after shutting down its output of 350,000 barrels a day in January after failing to agree an export fee with Sudan.

On Wednesday, Bashir said he was ready to meet Kiir after the African Union had urged both to hold a summit as soon as possible. Ethiopian Prime Minister Hailemariam Desalegn visited Khartoum and Juba this week to mediate between the presidents.

"Our president had sent him (Bashir) an invitation before which is still open and we believe our president has all along been open to a serious and meaningful meeting with the president of Sudan," South Sudan's Information Minister Barnaba Marial Benjamin told Reuters.

"Since the message was brought to us by His Excellency the Prime Minister of Ethiopia...we believe that President Omar al-Bashir will honor the meeting," Benjamin said.

He did not say when a meeting could take place. Delegations from both countries are scheduled to resume talks in Ethiopia in mid-January.

South Sudan seceded from Sudan under a 2005 peace agreement which ended decades of civil war. But both countries have yet to demarcate their disputed border which straddles oil production facilities.

They are also at odds over Abyei, a contested area between Sudan and South Sudan prized for its fertile grazing land.

(Reporting by Carlvins Odera; Writing by Ulf Laessing; Editing by Michael Roddy)