Wang said China and Japan should maintain momentum in the development of bilateral relations through mutual efforts such as high-level contacts.
The Trump-Abe discussions, the second of its kind between the two since previous year, would continue with a larger bilateral meeting where the leaders could expand their discussions to include a range of "priority bilateral issues", said the official.
"We confirmed Japan's plan to improve relations with China", Wang, who also holds the position of state councilor, told reporters after the meeting.
Chinese Premier Li Keqiang is set to visit Japan next month for a trilateral summit with Abe and South Korean President Moon Jae-in. The diplomats discussed the North Korea issue, their economic relations and territorial disputes in the East China Sea.
A senior government official did not confirm the media report, but said Abe wanted Motegi to accompany him to the U.S.to address trade issues, though this would depend on the situation in parliament, where the government faces criticism over suspected cronyism scandals. The Chinese are seeking Japanese cooperation on United States steel and aluminium tariffs implemented last month, the Japanese Kyodo News agency reported Saturday, citing people close to the talks.
Long-fraught ties between Tokyo and Beijing deteriorated to a 40-year low after the Japanese government's 2012 purchase of disputed islets near Taiwan sparked Chinese demonstrations, damaged trade and even raised fears of a military clash.
Kono told Wang that true improvement in bilateral ties can not be achieved without stability in the East China Sea, where China has challenged Japan's sovereignty over uninhabited islets.
Wang said the visit was a response to Japan's positive attitude toward China.
Kono met Wang in Beijing in January.
"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.
On Monday, Kono and Wang will co-chair a bilateral, high-level economic dialogue in which they are expected to discuss opportunities for economic cooperation including trade and investment.
Kono said that he hoped the first economic dialogue between the countries in eight years would be a "fruitful discussion".