Sweden, among others, faces the threat of tariffs if a purchase of the island is not allowed. If tariffs are imposed, the EU has threatened strong countermeasures.
Japan's Nikkei 225 index fell 1.1 percent in Tuesday's trading, while the broader Topix fell 0.8 percent.
The Hang Seng in Hong Kong is down 0.4 percent, while Shanghai is down 0.3 percent. Shenzhen is down further, 1.2 percent.
The Kospi in Seoul, on the other hand, is up 0.1 percent.
