"I hope that we will be able to discuss what and China can work together on in the global arena, not just bilateral issues", Kono told reporters on Friday.
Japanese officials said the mutual foreign ministers' visits for the goal of bilateral talks are the first between Japan and China in eight years.
"But together with Japan's efforts. we would like to bring China-Japan relations back on a path of sustainable and normal development".
"Since past year, Japan has, in relations with China, displayed a positive message and friendly attitude", Wang said at the meeting, adding that he hoped that the visit would help the two countries move towards better ties.
The world's second and third largest economies have a fraught relationship, complicated by longstanding maritime disputes and Japan's wartime legacy.
But Tokyo is eager to get the relationship back on firmer footing, especially as it fears being shut out of negotiations on North Korea's nuclear programme in which Beijing is likely to be a major player.
Kono said he also asked for China's cooperation in resolving the issue of North Korea's abductions of Japanese nationals in the 1970s and 1980s. Japan has come in for criticism from U.S. President Donald Trump on trade and been hit with tariffs on steel and aluminum, but Japan has not yet threatened counter-tariffs.
The two sides reportedly agreed to continue to fully implement all relevant United Nations resolutions and to work together closely in order to realize the dismantlement of the North's nuclear weapons and missiles.
Abe, who is due to meet with Trump in Florida on Tuesday to discuss North Korea, may also meet with Wang. The time is ripe for the two nations to improve relations to mark the 40th anniversary of their 1978 Treaty of Peace and Friendship, both ministers said.
"We agreed to carry out high-level visits, first with (Chinese Premier) Li Keqiang coming to Japan for a Japan-China-South Korea summit, then Prime Minister Abe visiting China and Xi Jinping visiting Japan", Kono told reporters after his meeting and working dinner with Wang in Tokyo.