TOKYO—In an action that could further strain ties between Tokyo and Beijing, Japan's national government is considering purchasing a set of islets at the center of a territorial dispute.

Prime Minister Yoshihiko Noda's remark that his government is weighing the nationalization of the privately owned property is the latest salvo in a longstanding diplomatic standoff with China. Both nations claim sovereignty over the Japanese-administered islands, called the Senkakus by Japan and Diaoyu by China.

"There...