BAGHDAD, Sept 3 | Mon Sep 3, 2012 1:57pm EDT

(Reuters) - A U.S. official has said firms should co-operate with Iraq's central government before striking oil and gas deals with the autonomous Kurdistan region, according to a statement from the Iraqi prime minister's office.

Baghdad maintains it alone has the right to export Iraqi crude. But Kurdistan has moved ahead with signing exploration deals with oil majors such as Exxon and Chevron, which the central government rejects as illegal.

"The United States has called on all the companies to (remember) the necessity to co-ordinate with the central government before concluding any deal or contract, especially in the fields of oil and gas," a statement from Prime Minister Nuri al-Maliki's office said on Monday.

The statement contained details of a meeting between the prime minister and Elizabeth Jones, U.S. Assistant Secretary of State for Near Eastern Affairs, on Sunday.

No one from the U.S. State Department was immediately available to comment.

Kurdish oil exports make up a fraction of Iraq's shipments, but the payment dispute feeds into a wider conflict between Iraqi Arabs and Kurds over autonomy, oil and land that risks upsetting Iraq's uneasy federal union.

Maliki said in July that U.S. President Barack Obama had backed Baghdad's concerns over Exxon Mobil's oil deal with Kurdistan in a letter. The White House declined to comment on its content.

Autonomous since 1991, Kurdistan runs its own government and armed forces but relies on the central government for a percentage of the country's oil revenues from the national budget.