"China also wants to create the environment of mutual concessions. It is important to have the environment of both sides making efforts to aim for the meeting," the source quoted Wang Jiarui, head of the International Department of the Communist Party's Central Committee, as saying when he held talks with Japanese opposition lawmakers on Monday in Beijing.
"Leaving this situation as it is will damage both countries," he was quoted as saying. "There are adverse effects on corporate activities and investment. We have to find a way out of the difficulties."
Wang, however, also told a delegation from the Social Democratic Party led by its chief Tadatomo Yoshida that Japanese Prime Minister Shinzo Abe first needs to make it clear what he wants to discuss with Chinese President Xi Jinping if a meeting with him becomes possible, according to the source, who spoke on condition of anonymity.
"There is no point in holding a meeting between the two leaders if the prime minister maintains his wrong position toward China," Wang said, according to the source.
Wang's remarks are believed to have been aimed at seeking some compromises or new approaches from the Japanese government over territorial and historical issues that have brought relations between the countries to their lowest point in many decades.
On Tuesday, when China's fourth-highest ranking Communist Party member Yu Zhengsheng met with the delegation of the small opposition party, he told it that whether bilateral relations can be improved or not depends on choices Abe makes in the coming months toward Beijing.
Yu, chairman of China's top political advisory body, said that for the leaders' meeting to be held on the sidelines of this year's summit of the Asia-Pacific Economic Cooperation forum in Beijing, Abe needs to change his stance on two issues -- the war-related Yasukuni Shrine in Tokyo and a group of Japan-controlled islets in the East China Sea.
Wang also attended the meeting between Yu and the Japanese delegation. Wang's remarks, likely reflecting the Chinese leadership's latest thinking toward Japan, have not been made public either by the Communist Party or Yoshida, who held a press conference after meeting with the two politicians.
Abe and Xi have yet to hold official talks since they each came to office more than a year ago.
Sino-Japanese relations, already strained over the Senkaku Islands, were further aggravated with Abe's December visit to the shrine, which honors Japanese leaders convicted as war criminals by an Allied tribunal along with millions of war dead.
Yu did not specify what exactly Abe needs to do when he met with the Japanese delegation, but what he meant was presumably similar to a message he conveyed to the Japanese government during a meeting last month with lawmakers from Abe's ruling party.
Yu told the delegation of the ruling Liberal Democratic Party that bilateral relations can be repaired if Abe promises not to visit the shrine again and his government admits the existence of a sovereignty dispute over the Senkakus, known as Diaoyu in China.
Since spring, senior Chinese officials have begun accepting various Japanese delegations and sending clearer signals that while the cause of soured ties boils down to Abe's political stance, Beijing is nevertheless willing to promote exchanges with Japanese companies, political parties and local government officials.
In the virtual absence of high-level government-to-government contacts between the two countries, a group led by Masahiko Komura, vice president of the LDP, also held talks with Zhang Dejiang, ranked third in the Communist Party's powerful seven-member Politburo Standing Committee, in May.
Komura told Zhang that Abe is hoping to hold an official meeting with Xi when the summit of the APEC forum takes place in Beijing.
In the latest in a series of visits from Japan, transport minister Akihiro Ota will be on a three-day visit to Beijing from Thursday. It is the first time for a Japanese minister to visit the Chinese capital since Abe's government was formed in December 2012.