The International Court of Justice (ICJ) in April ruled that Japan's whaling campaign in the Southern Ocean was a commercial venture and had no research value, which Tokyo said justified the hunt.
Japan called off its 2014-15 Antarctic season but Abe has since signalled that he intends to look at ways it can be resumed without breaching the ICJ ban.
Watson, who has spearheaded a decade of sometimes violent high seas opposition to the slaughter, said his letter was handed to Abe at a state dinner in Canberra yesterday by Australian Greens senator Peter Whish-Wilson.
"On behalf of the Sea Shepherd volunteers worldwide I would like to respectfully request that Japan abide by the ICJ ruling and that Japan respects both the moratorium on commercial whaling and the Southern Ocean Whale Sanctuary," the letter read.
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"If the Japanese whaling fleet returns to the Southern Ocean Whale Sanctuary in 2015, the ships and the volunteers from Sea Shepherd will also return to oppose any continued unlawful whaling activities."
The Canadian marine conservation group founder said "there is no need for this conflict to continue".
"Japan has no need to kill whales any longer. In fact whaling continues only because of subsidies from the Japanese government," he said.
"In return for ending whaling, Japan will gain the respect and admiration of conservationists around the world.
"I would like to see Japan become a great maritime conservation nation and to shed its present reputation as a nation that takes from the sea and gives nothing back," Watson added.