Aso, who is also Japan's finance minister, agreed with Chinese Vice-Premier Zhang Gaoli to strengthen "relations of trust," between their nations, the Kyodo news agency reported.
Zhang told Aso that the two sides should "push forward continued improvements in relations," according to China's official Xinhua news agency.
Ties between Beijing and Tokyo have warmed since last year, when China's President Xi Jinping held breakthrough talks with Japanese Prime Minister Shinzo Abe.
Aso is a former prime minister and remains a heavyweight in the ruling Liberal Democratic Party, which has taken a more nationalist tone under Abe.
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Strains over attitudes towards wartime history persist, with Beijing often accusing Abe's administration of whitewashing Japan's militaristic past.
Xi struck a friendly tone on relations when addressing a Japanese delegation in Beijing last month, but warned against "distorting" history.
China is preparing a massive military parade in September to mark the 70th anniversary of Japan's World War II defeat, also declaring it a public holiday.