Naval craft blew up one boat after the three were spotted near a restricted zone before chasing and sinking the other two, leaving an unknown number of casualties, the ministry said.
"Navy foils an LTTE (Tamil Tiger) attack at Colombo harbour, one LTTE boat destroyed at 5:30 am," the defence ministry said in an initial statement on its website, before later reporting the other two boats had also been sunk.
A foreign container vessel was damaged by the explosion of the first rebel boat hit by the navy, a military official said.
"A container had burst open and come off its original position as a result of the shockwaves," a military official said, adding the vessel was not hit by naval fire.
The ship was heading for a berth in Colombo port, officials said.
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Residents reported hearing gunfire near the port's high-security zone.
Unconfirmed reports said the authorities had arrested three fishermen over the incident and investigations were underway.
"The detection was initi