Tokyo-Moscow relations have been hamstrung by the row dating back to the end of World War II when Soviet troops seized the four southernmost islands in the Pacific Kuril chain, known as the Northern Territories in Japan.
Japan and Russia's lingering tensions have prevented them ever signing a peace treaty to formally end World War II hostilities, hindering trade and investment ties.
"This is a complex, multi-faceted issue that can only be resolved in a manner acceptable to both sides through an even deeper partnership between the two countries," Putin's chief foreign policy advisor Yury Ushakov said ahead of the visit.
His Russian counterpart Sergei Lavrov on a visit to Tokyo last month said Russia wants to "move forward" in relations, but is not prepared to budge on the "result of World War II".
Putin said during a public phone-in in April that he thinks "a compromise could be found at some point -- and it will be found" on the territorial dispute.
Moscow hopes the meeting will help create a "constructive atmosphere in bilateral relations", but "immediate serious progress" is unlikely, Kremlin spokesman Dmitry Peskov warned.
Russia has in turn angered Japan recently by building new modern compounds for its troops stationed on two of the disputed islands.
Russian Prime Minister Dmitry Medvedev also infuriated Tokyo by visiting one of the islands, home to some 19,000 Russians, last year.
Putin said last month he welcomed Abe's visit as it comes despite "pressure from (Japan's) partners, particularly the United States".
Abe will later this month host a summit of the Group of Seven advanced industrial countries, from which Russia has been excluded over its annexation of Crimea.
US President Barack Obama reportedly asking Abe in February to postpone his trip to Russia, according to sources quoted by Japan's Kyodo news agency.
Writing in pro-Kremlin daily Izvestia yesterday, a former deputy foreign minister and ambassador to Tokyo, Alexander Panov, suggested the meeting could see "Japan drop a number of sanctions" it imposed on Russia over Ukraine.
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