Abe and Xi have not held talks in the format of an official visit by either side since both men took office in 2012, but years of strain on bilateral relations due to historical and territorial grievances have recently given way to a thaw.
Now in the works is a free trade agreement between Japan, China, and South Korea, who together account for almost a fifth of global GDP. Mr Kono stressed that Japan and China share the same goal on North Korea. "We confirmed that we shall continue our close coordination while also completely implementing related UN Security Council resolutions to realise the irreversible, verifiable and complete denuclearisation of North Korea and its missiles".
Mr Wang said his visit was China's answer to "positive" messages and policies by Japan.
The visit by Wang, a veteran Japan handler who had served as an ambassador to Tokyo, comes as the world's second and third largest economies attempt to ease tension, caused by longstanding disputes over maritime claims and Japan's wartime legacy.
Chinese State Councillor Wang Yi, who will stay in Japan until Tuesday said he hopes that his visit could become an important step for bilateral relations to return to normal and create conditions for future high-level exchanges, reported Chinese state media Global Times.More news: Sir Patrick Stewart: Captain Picard would have voted Remain
More news: 5 of the greatest achievements by Indians at the Commonwealth Games
More news: What to know ahead of Sunday's severe weather — FIRST ALERT DAY
They also discussed the vision each country has for the wider region, namely Japan's "free and open Indo-Pacific" strategy and China's "One Belt, One Road" infrastructure megaproject.
Wang spoke to reporters in Tokyo on Sunday after his meeting with Japanese Foreign Minister Taro Kono.
The leaders of China and Japan are expected to pay reciprocal visits as relations between their countries warm, the Japanese foreign minister said on Sunday.
Wang on Monday holds high-level talks with Kono and other Japanese Cabinet ministers.