The two leaders spoke on the phone about Pyongyang's test which they agreed was "unacceptable", South Korea's Yonhap news agency reported.
The blast at the Punggye-ri nuclear site was the North's fifth and most powerful yet at 10 kilotons.
While Seoul and Tokyo regularly condemn the North's nuclear ambitions, their own relationship has been frayed at times due to territorial disputes and the legacy of Japan's harsh colonisation of the Korean peninsula from 1910-45.
The news of today's test drew swift condemnation from US President Barack Obama.
North Korea has been hit by five sets of UN sanctions since it first tested a nuclear device in 2006, but has insisted it will continue, come what may.
The nuclear programme has gone alongside a series of ballistic missile launches, the latest of which took place on Monday even as world powers gathered for a G20 meeting in China.
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