ExxonMobil has met officials from Iraqi Kurdistan, a statement said, after rare talks with Baghdad, which has decried a controversial deal between the US giant and the autonomous region.
The back-to-back meetings come amid a long-running dispute, of which Exxon is at the centre, between Iraq's central government and the northern Kurdish region over dozens of energy contracts signed by Kurdistan that Baghdad says are illegal,
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The meeting came a day after Tillerson held rare talks in Baghdad with Iraqi Prime Minister Nuri al-Maliki, who appeared to rule out production-sharing deals such as the one Exxon has signed with Kurdistan.
The US company's chief, in the meeting, apparently mentioned upcoming "important decisions", according to a statement issued by Maliki's office.
In October 2011, Exxon signed a deal for oil exploration with Kurdistan, angering the central government, which has said the American company must choose between its deals with Baghdad and with the autonomous region.
Exxon and Anglo-Dutch giant Shell had completed a deal in January 2010 to develop production at West Qurna-1, an oil field in south Iraq, but late last year, the US firm informed Baghdad that it wanted to sell its stake in the project, indicating it would focus on the controversial Kurdish deal.
The Exxon dispute is one of several between Baghdad and the Kurdish region -- the central government also regards other contracts signed by Kurdistan to be illegal because they were not expressly approved by the federal oil ministry.