There were no official reports about the source or size of the spill in the waters near the Al-Khafji field.
On Saturday Kuwait said various services were investigating the incident but did not give the magnitude of the spill near Kuwait's southern Ras al-Zour area nor its cause.
Kuwaiti authorities on Saturday were working on containing and cleaning up a crude oil spill in the country's southern waters in the Gulf, Kuwait Petroleum Corporation (KPC) said in a statement.
Ras al-Zour is where Kuwait National Petroleum Company (KNPC) is building the Middle East's largest oil refinery, with a processing capacity of 615,000 barrels per day and $11.5 billion worth of contracts.
However, Kuwaiti media on Sunday quoted local oil experts as saying the spill originated from an old 50-kilometre (31-mile) pipeline from Al-Khafji.
There's no immediate estimate of the number of barrels suspected to be spilled in the water.
Authorities said yesterday that beaches would be cleaned once power and water plants are secured and the spill is under control.
Saudi Arabia and Bahrain, located south of Kuwait along the Gulf coast, said slicks from the spill had not reached their waters.
Saudi Arabia, in a statement published by the official SPA news agency, said it had implemented a "crisis management plan" and was conducting an aerial survey of its oil installations along the coast.
The KPC said teams from Saudi Arabian Chevron and Oil Spill Response Limited (OSRL) had joined the coastal clean-up.