A spokesman for the Kuwait Oil Co (KOC), Saad al-Azemi, said on Twitter that "average production reached 1.1 million" barrels in Kuwait today.
Daily production in OPEC's fourth largest producer is normally around 3.0 million barrels per day.
Azemi also said natural gas production was at 620 million cubic feet, down from Kuwait's daily average of more than 1.3 billion cubic feet.
The strike comes as world oil producers gathered in Qatar aiming to negotiate an output freeze to boost prices.
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"Observed since 7:00 am (0930 IST), this open-ended strike will continue until the workers' demands are met," Qahtani said.
The cabinet strongly criticised the "unacceptable" strike, calling it a "clear violation of the law", and demanded legal measures against those involved.
The government also urged Kuwait Petroleum Corp (KPC) to mobilise the manpower needed to ensure continued production.
Yesterday, the union turned down an appeal from Kuwait's acting oil minister, Anas al-Saleh, to call off the strike.
As the strike began, KPC 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 agency's website.
He urged Kuwaitis "not to listen to rumours that the strike has affected the needs of the local market".
He said reserves of gasoline and petrol derivatives were "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 said workers had boycotted negotiations called for Thursday by the social affairs and labour ministry.