Since an awkward 2014 encounter between Abe and Xi on the sidelines of a summit, there have been ministerial visits by both sides and a softening of rhetoric. Furthermore, Japan would like to take advantage of China's huge population.
Abe said he sought frank talks with Xi and Li covering North Korea and trade issues.
He also told Li that "the worldwide community, including Japan, is watching carefully the human rights situation in China". "In other words India, Japan plus one", said Gokhale.
But his meeting with Xi on Friday will be the first full-scale Sino-Japanese summit since 2011.
In a special gesture, Prime Minister Narendra Modi will be hosted by his Japanese counterpart Shinzo Abe for a private dinner at his holiday home in the picturesque Yamanashi prefecture on October 28, which will be, perhaps, the first such reception to be extended to a foreign leader.
China is Japan's main trading partner, with bilateral trade reaching $300bn past year.
According to Abe, relations between the two countries are in the "abnormal state".
He said the foremost of these would be how to leverage Japan as a development aid partner for India's economic modernisation and flagship development programmes such as Skill India, Make in India, and Digital India, as also the Mumbai-Ahmedabad high-speed rail project.
Mr Abe also said Tokyo was "determined" to normalise diplomatic relations with Pyongyang, but only if preconditions were met, including denuclearisation and the release of kidnapped Japanese citizens.More news: Jamie Lee Curtis' Boast About 'Halloween' Opening Is Scary Good For Women
Japan and China, in building a strategic and mutually beneficial relationship, have the responsibility to properly deal with those issues and steadily develop their friendly and cooperative ties from the big picture, he noted. This year is the 40th anniversary of the signing of the Treaty of Peace and Friendship between Japan and China.
In the last decade, the nadir of relations between China and Japan was August and September 2012, when anti-Japanese demonstrations in several cities in China turned violent.
The incident prompted anti-Japanese riots in China, and kicked off a frosty spell that has only recently begun to thaw.
"If Xi promises to come to Japan next year, that would be very big", said Mr Kiyoyuki Seguchi, research director at the Canon Institute for Global Studies in Tokyo.
In the past year, China has stepped up its outreach to Japan and others as it locked horns over trade with the United States.
"China is willing to work together with Japan to take Sino-Japanese relations back to a normal track, maintaining stable, sustainable and healthy development and making new progress", Li said during an appearance with Abe on Friday. This was because the TPP was seen by Tokyo as the economic inculcation of the USA economy into the region to match America's extensive network of alliances and security partnerships that can be found throughout North and Southeast Asia.
But as Trump's tariffs bite, China has increasingly looked to Japan to serve as a hedge against growing USA protectionism.
Yuichiro Tamaki, the leader of an opposition party, said that even some younger lawmakers in Mr Abe's ruling Liberal Democratic Party are cautious about the relationship.
Kunihiko Miyake, a former Japanese diplomat who is now visiting professor at Ritsumeikan University, said: "Nobody thinks ties with China have completely recovered, and they shouldn't think that".