"It is difficult to say what meetings will take place in 2016, but Russia is open to a dialogue with Japan at all levels," Afanasiev said at the Japan National Press Club in Tokyo.
Earlier in December, Japanese Foreign Minister Fumio Kishida said that the two countries would keep on seeking opportunities for dialogue at the highest level and had not ruled out Abe possibly visiting Russia.
According to Afanasiev, conclusion of a peace treaty between Japan and Russia requires the development of a wide network of contacts between the two countries.
"Of course, any restrictions on these contacts and bilateral ties do not help, and the more we have contact and links, the better it is for solving this problem," the envoy said.
He added that ties should be developed in various fields to promote mutual trust between the two countries.
"We need a political consensus in both Russian and Japanese societies to find a solution to the problem," Afanasiev said, adding that bilateral cooperation was mutually beneficial for Tokyo and Moscow.
Japan and Russia never signed a permanent peace treaty after World War II because of a disagreement over four islands, which Russia calls the Southern Kurils and Japan the Northern Territories. The disputed islands, located in the Sea of Okhotsk, were claimed by Soviet forces at the end of WWII.