Boats and crews have been putting booms into the water to try and contain the spill. According to the state-run Kuwait News Agency, the authorities' priorities were first to secure waterways, power plants and water facilities.
There's no immediate estimate of the number of barrels suspected to be spilled in the water.
In a statement later on Saturday, Khafji Joint Operations said no oil leak had been detected in its operation area after reports suggested the spill originated from a 50km pipeline at the shared oil field between Kuwait and Saudi Arabia.
The joint operations center in the Saudi border town of Khafji said facilities there have not been affected by the spill.
But Khaled al-Hajeri, the president of Kuwait's Green Line Society, has accused the government of covering up the full scale of the spill, saying the authorities already knew about the leak on Thursday.
Gorkhaland protests: GJM leaders to meet Home Minister on Sunday
Two top leaders of the Gorkha Janmukti Morcha, which has been ruling the autonomous hill council, Bimal Gurung and Roshan Giri, did not attend today's meeting.
Tourists and residents in Kuwait should stay way from the resort area called al-Khiran in Kuwait.
"This media blackout is intentional, and wrong. This will have an impact on the fish, the food people consume, and it directly affects their health and safety".
Sheikh Talal said precautionary measures had been taken around vital installations in Al Zour where a huge US$30 billion (Dh110.2bn) oil complex - including a 615,000-barrel-per-day refinery - is being built.
The Kuwait Petroleum Corporation said teams from Saudi Arabian Chevron and Oil Spill Response Limited were cleaning the coastal waters.
Tiny Kuwait, an OPEC member nation, has the world's six-largest estimated oil reserves.