In Tokyo, the two leaders discussed a possible peace treaty and agreed that fostering economic cooperation would help create the conditions to reach some future agreement on the island chain.
Mr Abe, speaking at a luncheon with Mr Putin, said they had agreed on "more than 60 projects" in economic-related areas, with details to be announced at a news conference later in the day.
What are the Southern Kuril Islands?
Russian Federation wants to attract Japanese investment, particularly to its far east. Japan hopes that stronger ties through joint economic projects will help resolve the thorny territorial issue over time. "The fundamental interests of Russian Federation and Japan require a long-term deal".
As the two leaders headed for their second round of talks on Friday, right-wing activists circled the streets in trucks.
2016: Putin meets Abe in Japan for talks on the territorial issue.
"But how to do this is a hard question", he told Japanese media.
But Tokyo has said it would not agree any economic cooperation with Russian Federation that would undermine the sanctions.
Mr. Abe and Mr. Putin spent much of their time on Thursday discussing small steps to move forward on the territorial dispute that has prevented their countries from signing a peace treaty to end World War II.
"We also tasked the relevant ministries to work out a range of new agreements in the investment, tax and labor sectors", the president said. Putin said the sides discussed the issue of allowing visa-free visits for the Japanese citizens, who used to be the citizens of the South Kuril Islands, to the tombs of their ancestors.
A statement released after their talks in Tokyo on Friday said the leaders "reached a mutual understanding that starting talks on the joint economic activities by Japan and Russian Federation. could be an important step" toward signing a peace treaty to formally end hostilities from World War II - an effort that has been stalled by the island row.
"There are security issues", Putin said.
The Russian leader made his first presidential visit to Japan on Thursday, meeting Japanese Prime Minister Shinzoa Abe.
Kyodo news agency also reported that the statement did not directly refer to the issue of the islands' sovereignty and said both sides agreed that joint economic activities would not compromise either of their positions regarding a peace treaty.
There are hopes of achieving a breakthrough over the territory off Japan's northern coast seized by Soviet troops in 1945.
Abe did not say if there was any progress on the territorial issue. The decision to incorporate in the document the expression "will not violate the two countries' sovereignty" is in line with Japan's assertion.
Putin has proposed free border movement of Sakhalin Region and Japan's Hokkaido Island residents.
"I think it is more the Japanese are trying to hedge their bets against the Chinese and perhaps, sort of, put a crack into the Russian Chinese defense relationship that has emerged in the last four or five years", Newsham said.
"The atmosphere in the meeting was very good, " Abe said. It was originally believed that Putin and Abe would converse in the hot springs outlooking a Japanese garden, before going to an observatory.
"Return the islands" and "Putin go home" was played out via loudspeakers.
Japanese Prime Minister Shinzo Abe will host Vladimir Putin on the Russian leader's first official visit to a G-7 country since Russia's 2014 annexation of Crimea at a hot spring in his ancestral city of Nagato on Thursday.