Kazakhstan's government has said that the deadline for talks with an Eni-led consortium about the Kashagan oil field has been delayed until 15 January.
"We have agreed with everyone but Exxon," Kazakh energy minister Sauat Mynbayev told reporters.
The government wants compensation for rising costs and the delay in the start of production at Kashagan.
Kazakhstan is also seeking an increase in the state oil and gas company KazMunaiGas's stake in the project.
Sources familiar with the situation said last week that the consortium had agreed to pay Kazakhstan between $2bn and $4bn (£1bn to £2bn) in compensation.
Stake value
Italy's Eni, the operator of Kashagan, has an 18.5% stake in the project, the same as Royal Dutch Shell, Total and ExxonMobil.
ConocoPhilips holds a 9.26% stake, with KazMunaiGas and Japan's Inpex having 8.33% each.
Exxon said last week it was not opposed to KazMunaiGas increasing its stake, but continued, "to work with the Republic of Kazakhstan to seek an amicable solution on the appropriate value for the equity".
But Mr Mynbayev said on Monday that Exxon's offer, "bears risks for the project".
The giant Kashagan oil field was due to start pumping oil in 2005, but now the date is set for 2010.
The project costs have jumped to $136bn from $57bn.
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