SEOUL—North Korea state media on Thursday issued a statement that claimed possession of all waters around South Korea-controlled Yeonpyeong Island, clarifying for the first time that its Nov. 23 attack of the island was motivated by a different view of the inter-Korean maritime boundary in the Yellow Sea than is widely held.

North Korea has said since the attack that it was motivated because shells from an artillery test South Korea conducted on the island that day fell into its waters.

Military...