The treaty between the two countries, if signed, would become a basis for resolving a dispute on Kuril islands located between Russian Federation and Japan, Al Jazeera reported.
Japan and Russian Federation are holding talks aimed at settling a dispute which has marred relations for more than 50 years.
"Relations between the two countries have been smoothly developing since the Japan-Russia summit two years ago in Nagato", said Abe.
Indeed, with the United Kingdom and South Korea in attendance, Japanese support could be crucial to a multilateral investment plan in Eastern Russian manufacturing and energy, for which President Putin is aiming.
Russian President Vladimir Putin on Wednesday said North Korea must be given security guarantees in exchange for steps towards denuclearisation.
These were occupied by the old Soviet Union in 1945 but have always been claimed by Japan.
He was speaking shortly after Mr Abe had urged him to move stalled negotiations on the islands, asking "If we don't do that now, when will we?" and "If we don't do that, who will?" "We are both fully aware that it will not be easy".
Beijing and Moscow have developed a "strategic partnership" reflecting their shared opposition to the "unipolar" world, the term they use to describe perceived USA global domination. "And then we will continue to address all controversial issues as friends based on the peace treaty", the president went on. "It is called trolling".
Abe, who said on Monday that talks with Putin were moving toward a peace treaty, did not give a response. "Putin does not expect anything", Kunadze told Echo of Moscow radio station.
Abe smiled at the suggestion. "This stance hasn't changed".
Mr Xi agreed with Mr Putin on Tuesday that their countries will safeguard global peace and stability as bilateral ties have "entered a new period of higher-level and faster development". The conference, conceived by Putin, is focused at heartening foreign investment, The New York Post reported.