"Serious negotiation about the future could occur if Pyongyang does not engage in any more provocative actions," Kerry told his Japanese and South Korean counterparts on Sunday.
Sunday's three-way meeting followed North Korea's fifth underground nuclear test earlier this month and an increased pace of regular missile firings - "the latest reckless choices Kim Jong-un has made," Kerry said.
South Korean Foreign Minister, Yun Byung-se, appeared reluctant to consider negotiations with North Korea, in view of Pyongyang's repeated defiance of UN Security Council resolutions and sanctions, Voice of America news reported.
Yun called for the current UN General Assembly which begins in 71st session on Monday, to "send out a united and forceful message," and impose even more robust sanctions on North Korea as it is "now at the final stage of nuclear weaponisation".
Japanese Foreign Minister, Fumio Kishida, also urged stronger pressure to be applied on Pyongyang "including further sanctions, as well as taking our measures respectively".
A joint statement issued by the three countries noted the ministers "explored ways to work together to ensure that all countries fully and effectively implement all their obligations and commitments under UN Security Council 2270, which imposed the strongest sanctions ever placed upon North Korea."