The strike, which could slash production if prolonged, comes as world oil producers gather in Qatar to negotiate an output freeze to boost prices.
"Thousands of workers began their strike," the oil workers union chief Saif al-Qahtani told AFP, adding that production was partially halted without clarifying which sites had been affected.
"Observed since 7:00 am (0300 GMT), this open-ended strike will continue until the workers' demands are met," Qahtani said.
On Saturday, the union turned down an appeal from Kuwait's acting oil minister, Anas al-Saleh, to call off the strike.
Hit by the sharp drop in crude prices on world markets, Kuwait is introducing a new payroll scheme for all public employees and wants to include the country's 20,000 oil workers, which would mean an automatic cut in wages and incentives.
As the strike began, Kuwait Petroleum Corp spokesman Sheikh Talal Khaled al-Sabah said that the national oil conglomerate had activated an "emergency plan" to ensure that local and international markets were not affected by the walkout.
"Export operations are going ahead as planned and (KPC) is capable of responding to major international market demands, based on agreements with clients," he said in a statement published on the KUNA news site.
The plan ensures that all petrol stations will continue to be supplied as well as Kuwait's international airport and companies operating at the facility, he said.
He urged Kuwaitis "not to listen to rumours that the strike has affected the needs of the local market," adding that Kuwait's "reserves of gasoline and petrol derivatives is enough to meet the country's demands for 25 days and strategic reserves could suffice for 31 more days."
KPC had offered to suspend all spending cuts if the union agreed to join a committee to negotiate a settlement.
But the conglomerate said workers boycotted negotiations called for Thursday by the social affairs and labour ministry.
The union is also protesting plans to privatise parts of the oil sector.
Kuwait, OPEC's fourth largest producer, currently pumps three million barrels per day.
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