Abe will not hold talks with Moon unless Seoul takes constructive steps over World War-Two era forced labourers and other issues, the Japanese daily said on Monday.
Abe will also forgo meeting Moon during other opportunities, including an Association of Southeast Asian Nations meeting in Oct. and an Asia-Pacific Economic Cooperation gathering in Nov. for the same reason, the Sankei said.
Relations between Japan and South Korea are arguably at their lowest since the countries normalised ties in 1965 as they spar over compensation for wartime forced labourers and recent export curbs imposed by Tokyo.
Japan tightened restrictions on exports to South Korea of important high-tech materials used for making memory chips and display panels, citing what it has called inadequate management of sensitive items by its Asian neighbour.
The curbs were seen as a response to South Korean court rulings ordering Japanese companies to compensate wartime forced labourers.
Japan says the decision violated international law because the issue of compensation was settled under the 1965 treaty that established diplomatic relations between the two nations after World War Two.
"Things might be at their worst since the normalisation of diplomatic relations," the Sankei quoted an unidentified source close to Abe as saying.
Abe and Moon also did not meet on the sidelines of the Group of 20 leaders' summit in Osaka in June.
Adding to the export curbs, Japan is preparing for Cabinet approval as early as Aug. 2 to remove South Korea from a so-called white list status with minimum trade restrictions, Japanese media have reported.
South Korea has protested against the plan, saying it would undermine their decades-old economic and security cooperation and threaten free trade. (Reuters)