The South Korean Defense Ministry said talks are under way on holding a joint drill between South Korea's Navy and the U.S. aircraft carrier Carl Vinson, amid rising tensions over North Korea's missile and nuclear programs.

"As for the exercise, talks are currently under way," ministry spokesman Moon Sang Gyun said during a press briefing, when asked whether the Navy would hold a joint exercise with the nuclear-powered aircraft carrier that is reportedly nearing the Korean Peninsula this week.

The development comes after Japan and the United States started a joint naval drill in the Western Pacific on Sunday involving two Japanese destroyers and the U.S. carrier, according to the Japanese Maritime Self-Defense Force said.

Concerns are growing that North Korea may conduct further test-firings of missiles or a sixth nuclear test around the 85th anniversary of the founding of the Korean People's Army on Tuesday.

Moon said the South Korea and U.S. militaries are at their highest possible readiness to cope with a nuclear test. He declined to elaborate further.