The two leaders "confirm that the relationship between Japan and the UK is the best it has ever been."
"Our two countries are natural strategic partners, sharing a common global vision of peace, security and international prosperity based on sustainable development and respect for human rights and the rule of law.
"We have shared interests in combatting key global challenges, including the areas of international society, counter-proliferation, climate change and poverty reduction," they said.
"We intend to cooperate more closely to strengthen counter-proliferation efforts, including through enhanced consultation and co-ordination over North Korea and Iran."
"We express our grave concern over the recent developments on the Korean Peninsula including the missile launch and the proclaimed nuclear test and urge North Korea to comply" with the United Nations Security Council resolution.
The pair also expressed "our deep concern at Iran’s failure to take steps required by the IAEA (International Atomic Energy Agency) Board and the UN Security Council, including a full suspension of all uranium enrichement related and reprocessing activities."
The statement also referred to cooperation on climate change, development aid and cultural and technological exchanges. Britain welcomed Japan’s efforts to more closely cooperate with NATO.