Exxon sent Baghdad into a fury at the end of last year by signing up for six KRG exploration blocs. The central government holds that any oil contracts signed with Kurdistan are illegal.
The U.S. major, also leading a project at the supergiant West Qurna-1 oilfield in southern Iraq, has sent two letters to the oil ministry confirming its decision to freeze its Kurdish deals.
Deputy Prime Minister for Energy Hussain al-Shahristani said on a visit to London that the company made clear it would only proceed if Baghdad approved its KRG contracts.
Shahristani has indicated many times that such approval was unlikely to be granted.
As for Exxon, they have sent a letter to the ministry of oil confirming that they will not take any action on the ground until their contract is approved by the Iraqi government, he said at a conference.
Baghdad has threatened to exclude Exxon from its upcoming exploration round and Shahristani said a decision had yet to be made on whether it could take part.
A long-running dispute between Iraq's central government and the KRG over land and oil rights has worsened in recent weeks and Arbil halted oil exports at the start of April.
Shahristani said Baghdad is prepared to discuss serious differences with the Kurdistan Regional Government (KRG) over oil matters, but said they would take time to resolve.
The high-ranking Iraqi official also confirmed that talks were taking place between BP
The UK major is looking closely at a project to revive the giant, ageing oilfield. Baghdad is understood to be keen to have the British oil major positioned in northern Iraq to counter the recent controversial move by Exxon into Kurdistan.
(Reporting by Simon Falush; editing by Jason Neely)