The Italian energy company noted the meeting took place in "the usual climate of friendship."
Redevelopment of Zubair will come through a $20 billion investment throughout the life of the 20-year contract, Eni said in January after winning the rights to explore the field.
Eni said production at Zubair would reach 1.2 million barrels of oil equivalent per day at full capacity. Production at the field has increased from 183,000 barrels of oil per day to more than 201,000 bpd, which the company said was the minimum needed to trigger cost recovery.
Production at the Zubair oil field is carried out by the Eni-led consortium, Zubair Technical Service Contract, which includes Iraq's Missan Oil Co., Occidental Petroleum Corp. and Korea Gas Corp.
Target production at Zubair is expected to be reached within six years.