The statement from the official, Hussein al-Shahristani, said the central government had cautioned Exxon against pursuing oil deals in Kurdistan, which the government says will remain illegal until long-awaited rules can be worked out to split revenues among Iraq’s fractious regions.

Mr. Shahristani’s office issued the statement a day after The Financial Times reported that Exxon, based in Irving, Tex., and the United States’ largest petroleum company, had become the first major international oil operator to sign a contract in the Kurdistan region — a move the company has neither confirmed nor denied.

If Exxon did indeed sign a deal in Kurdistan, it is wading into a central controversy that has dogged Iraq since the American invasion.

Oil has long been the heart of Iraq’s wealth, and the invasion threw control of the rich reserves into question, exacerbating longstanding enmity between the Kurds and other Iraqis. Under President George W. Bush, the passage of an oil law to split revenues was considered a crucial benchmark to bring long-term peace to Iraq.

Many smaller oil companies, including American ones like Marathon and Hunt of Texas, have signed contracts with the Kurdistan Regional Government. But the larger companies had held back to ensure they retain deals for fields in the south.

Michael Klare, a professor at Hampshire College and an authority on the Iraqi oil industry, speculated that Exxon might be betting that Iraq would not make good on threats of punishment, recognizing that the company’s investment elsewhere in the country was crucial to its economic revival.

“Both Exxon and the Iraqis understand that Iraq has no hope of reaching its lofty goals of higher oil output without Exxon’s involvement,” Professor Klare said. “Threats to punish the company for investing in the Kurdish area are hollow.”

Critics of the oil companies that went to Kurdistan after the overthrow of Saddam Hussein’s government say they are pursuing development in a manner that, far from contributing to stability through economic growth, has heightened ethnic tensions between Arabs and Kurds.

Exxon’s spokesman, Alan T. Jeffers, said Saturday in an e-mail that the company would not comment on whether it had signed an oil deal in Kurdistan, or respond to the Iraqi deputy prime minister’s statement. The Kurdistan Regional Government also had no immediate statement, though its official Web site prominently posted, without clarification, the text of The Financial Times article.

For now at least, the Iraqi government appears to be taking a strong, but somewhat vague, stance. “The Iraqi government will deal with any company that violates the law the same way it dealt with similar companies before,” the deputy prime minister’s statement Saturday said.

In the past, the government has excluded oil companies active in Kurdistan from new auctions elsewhere in Iraq. It was unclear whether the statement implied any threat to revoke Exxon’s existing contracts, which would be significant. A spokesman for Mr. Shahristani declined to elaborate.

The actual legal argument against any deal remains a matter of controversy. Iraq’s Constitution allows regions to strike their own oil deals, but the central government says there is no current law spelling out how that can happen.

Beyond the ripples that oil deals send through Iraq’s fragile politics, they are important for bringing new oil to world markets — but only if the relations between companies and the government go smoothly enough to allow investment.

The State Department and the military have sought to tamp down antagonism between Kurdistan and the central government for years, and American troops have died trying to keep the peace along that internal border.

With the American withdrawal imminent, concerns are mounting that ethnic tensions could again threaten stability.

Under a 2009 contract, Exxon is leading a consortium developing one of Iraq’s largest oil fields, outside Basra near the Persian Gulf.

Exxon and its partners agreed to invest $50 billion over seven years to increase output by about two million barrels of oil per day there, at West Qurna Phase 1, bringing more new oil to market than the United States currently produces in the Gulf of Mexico. Margins, though, are low. Kurdistan offers more lucrative production-sharing agreements, allowing the company to earn a larger share of revenues and to count more of the crude on its books, which helps boost stock prices.

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