The remarks came as Kono held his first meeting with Wang since assuming office on Thursday.
Both senior diplomats met on the sidelines of a series of foreign ministers meetings among the 10 Southeast Asian nations.
Earlier on Monday, top diplomats of the United States, Japan and Australia said in a joint statement that they "voiced their strong opposition to coercive unilateral actions that could alter the status quo and increase tensions" in the South China Sea.
Japan was urged to note that the overall situation in the South China Sea continues to improve, and Japan should respect the efforts made by China and ASEAN countries, Wang said.
Kono said Japan attaches importance to China, and the two countries could make important contributions in revitalizing Asia and promoting world peace by working hand-in-hand.
Wang said China hopes Japan matches its words with actions and translates its positive stance about improving the ties with China into tangible policies and actions.
Tokyo should not always claim its readiness to improve the ties and then make trouble for China soon after, Wang added.
Kono assumed his new role as top Japanese diplomat after Japanese Prime Minister Shinzo Abe reshuffled his Cabinet on Thursday.
His new post attracted observers' optimism about the future of the fragile China-Japan ties partly because his father, former lower house speaker Yohei Kono, is known for supporting friendship with China.
The elder Kono issued the landmark Kono Statement in 1993 in the capacity of chief cabinet secretary to admit that the Imperial Japanese Army forcibly recruiting "comfort women"－a euphemism for sexual slaves－during World War II.
Wang told Kono his father is a politician with historical conscience and independent personality, and the father has dedicated great effort over many years promoting China-Japan friendship.
Wang said it is hoped the new foreign minister brings with him the correct perceptions of his father and makes efforts to realize real improvements of the ties during his tenure.
