The great Iraqi oil rush has started to exacerbate dangerous communal tensions after a major oil company ignored the wishes of the central government in Baghdad and decided to do business with its main regional rival.

The bombshell exploded last month when Exxon Mobil, the world's largest oil company, defied the instructions of the Baghdad government and signed a deal with the Iraqi Kurds to search for oil in the northern area of Iraq they control. To make matters worse, three of the areas Exxon has signed up to explore are on territory the two authorities dispute. The government must now decide if it will retaliate by kicking Exxon out of a giant oilfield it is developing in the south of Iraq.

Political leaders in Baghdad say the company is putting the unity of their country at risk. Hussain Shahristani, the Deputy Prime Minister in charge of energy matters, told The Independent in an interview in Baghdad that any oil or gas field development contract in Iraq "needs the approval of the federal government, and any contract that has not been presented to the federal government has no standing and the companies are not advised to work on Iraqi territory in breach of Iraqi laws".

Baghdad has had oil disputes before with the Kurdistan Regional Government (KRG), but the present row is far more serious because it is the first time "Big Oil" has moved into Kurdistan, showing that at least one of the major oil companies is prepared to disregard threats from the government of Nouri al-Maliki. Previously, only small independent foreign oil companies, without other interests to protect in the rest of the country, have risked signing contracts with the Kurds.

"Exxon Mobil was aware of the position of the Iraqi government," says Mr Shahristani, a former nuclear scientist who was tortured and imprisoned by Saddam Hussein. "We hear from the American government that they've advised all American companies, including Exxon Mobil, that contracts should not be signed without the approval of the federal government."

Whatever the prospects of finding oil in the north of Iraq, observers are surprised that Exxon is prepared to hang its future in Iraq on the outcome of the power struggle between Iraqi Kurdistan and the central government. Control of the right to explore for oil and exploit it is crucial to the authorities on both sides since they have virtually no other source of revenue.

The Kurds have won a degree of autonomy close to independence since the fall of Saddam, and the ability to sign oil contracts without reference to Baghdad will be another step towards practical independence and the break-up of Iraq. A parallel would be if the Scottish government were to sign exploration contracts in the North Sea without consulting London.

What makes the Exxon-KRG deal particularly inflammatory, says Mr Shahristani, is that three of the six blocs where Exxon is planning to drill are understood to be "across the blue line – that is outside the border of the KRG". This means they are in the large areas in northern Iraq disputed between Arabs and Kurds since 2003, but where the Kurds have military control.

The government must now decide if it will make good on its threats and replace Exxon at a mammoth oil field called West Qurna 1 at the other end of the country, north of Basra. Iraqi oil officials hint that Royal Dutch Shell might replace the American company.

Both sides have much at stake. The Iraqi government is totally reliant on its oil revenues to pay its soldiers, police force and civilian officials. It needs vast sums to rebuild the country after 30 years of war, civil war and sanctions. In 2009, it began to expand its oil industry by signing contracts with firms such as BP, Royal Dutch Shell and Exxon to boost production in under-exploited and poorly maintained fields.

These companies thereby gained access to some of the largest fields in the world, each with reserves of more than five billion barrels. Vast sums are being invested, mostly around Basra in the south of Iraq. Oil output, now at 2.9 million barrels a day, is due to rise to a production capacity of 12 million b/d by 2017, potentially putting Iraq on a par with Saudi Arabia as an oil exporter.

Mr Shahristani is pleased with progress so far, saying that what "we are doing in Basra is at least five times larger than the largest oil projects in the history of the oil industry so far."

Sitting in his vast office in a cavernous palace originally designed for one of Saddam's senior lieutenants, he holds up a chart showing the surging production from the Rumaila oilfield of 1.4 million b/d, more than Britain's entire current output of crude from the North Sea.

Iraqis are split on whether Exxon is being cunning or naive. One explanation is that the oil company feels so powerful, or so essential to Iraqi oil development, that it can disregard the Iraqi government. An alternative argument is that Exxon is dissatisfied with the West Qurna 1 deal and so does not mind walking away from it and looking for oil elsewhere. A third is that the company got suckered by the Kurds.

Iraqi Arabs know that the Iraqi Kurds want to control as much of Iraq's oil reserves as possible to buttress their independence. Less easy to understand is why Exxon should willingly make its activities a central issue in the Arab-Kurdish confrontation which has for so long destabilised Iraq.

Flashpoint: Iraqi military bases

The transfer of Iraq's military bases to local control is another flashpoint between the Kurdistan Regional Government and Baghdad, and some fear the dispute may boil over when US forces pull out at the end of the year.

Last month saw a tense standoff between the Iraqi army and local Kurdish forces at a US airbase in the northern city of Kirkuk, an oil-rich area long a point of dispute. The Kurdish police force reportedly blocked an army team from entering the base for an official handover from the US, unhappy that it was being transferred to Baghdad.

In an effort to calm the drama, the US ambassador, James Jeffrey, met Kirkuk's Governor, Najmaldin Karim, and Iraq's Prime Minister, Nouri al-Maliki, in the capital.

"We did not want a situation where we ended up shooting at each other," said Mr Karim.

The situation was defused when the central government made assurances that the base would be used for civilian aircraft only, a key demand of the Kurds.

However, once the base is handed over to Iraqi control, Washington will have little control over whether Baghdad sticks by its verbal agreement. Indeed, Ali Ghaidan, the commander of Iraq's ground forces who led the army team that eventually entered the base, has since publicly ruled out the possibility of the base being turned into a civilian airport – saying it is of too much strategic importance to Iraqi forces.