Final answer:
Russia has control over the Kuril Islands, including the southernmost islands, that are disputed with Japan.
Step-by-step explanation:
The country that has the Kuril Islands, including the southernmost islands, that are disputed with Japan is Russia. Japan claims the southernmost islands of the Kuril Island chain, known as the Northern Territories in Japan.
The dispute between Japan and Russia over the Kuril Islands dates back to the end of World War II. In 1945, the Soviet Union took control of the islands, and ever since, Japan has claimed sovereignty over the southernmost islands.
Despite negotiations and offers, the issue remains unresolved, and Russia currently maintains control over the Kuril Islands.