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Japan's Prime Minister Shinzo Abe held a telephone summit with South Korean President Lee Myung-Bak, Jiji Press said.
South Korea chairs the United Nations Security Council this month.
"At the United Nations Security Council, we should adopt a resolution to strengthen the sanctions" against North Korea, Abe told Lee, according to Jiji.
Lee agreed with Abe, saying: "We need a strong resolution. South Korea and Japan need to cooperate" over the issue, Jiji said.
North Korea confirmed it had "successfully" carried out an underground nuclear test, drawing immediate condemnation from South Korea, Japan, the United States and UN leader Ban Ki-moon.