MOSCOW (Dow Jones)--U.S. oil company Exxon Mobil Corp. (XOM) is against Kazakhstan's state-owned Kazmunaigas raising its stake in the offshore Kashagan project, the Interfax news agency reported Tuesday, citing Kazakh Energy Minister Sauat Mynbayev.

"The optimal solution for Kazmunaigas is to increase its stake to become the project's largest shareholder. Whether this is possible is another matter," he said, adding that negotiations are continuing.

The Kashagan consortium, led by Italy's Eni SpA (E), has been embroiled for months in a disagreement with Kazakh authorities over rising costs and delayed production at the field.