Blair met Shinzo Abe, his Japanese counterpart, on Tuesday and the two agreed to work more closely to press North Korea to abandon nuclear weapons.
Abe said: "We saw eye-to-eye on the need to induce North Korea to abandon nuclear weapons, on the need to apply the necessary pressures."
Blair's office said the two leaders also held discussions on Iran's nuclear programme and the conflicts in Iraq and Afghanistan.
Güncelleme Tarihi: 20 Eylül 2018, 18:16"I said to the prime minister [Abe] I would work closely with him and with the Japanese government in doing our best to bring this about," Blair said.
Blair welcomed Tokyo taking its "proper place" on the global stage. "I believe the moment is ripe for this to happen," he said, adding that Japan's inclusion in the council was "long overdue".
Japan played a crucial part in recent six-party talks over North Korea's nuclear weapons programme, was key to global talks on climate change and provided troops in southern Iraq, where they worked alongside British forces, Blair said.
Japan's bid in 2005 to gain a permanent council seat failed to secure the required two-thirds support from the General Assembly. Abe, however, has pledged to chart a bolder diplomatic path than his predecessors.
He will also meet German, French, European Union and Nato leaders on his January 9-13 trip, his first to Europe since taking office in September.
"I would like to seriously pursue an assertive diplomacy through these visits. I would like to convey in what direction Japan will be heading ... and demonstrate Japan's will to actively contribute to the world,'' Abe said.