When investors had lunch in Tokyo, the Nikkei 225 was down 0.4 percent, while the broader Topix index was up about the same amount.
The Hong Kong stock exchange's Hang Seng fluctuated around zero, as did Shanghai's composite index. Shenzhen's equivalent pointed to a plus of 0.3 percent.
In South Korea, the development was more pessimistic, with Kospi at minus 2.9 percent. Taiwan's weighted index was simultaneously at minus 0.5 percent.
Trump signed a presidential order overnight on specific tariffs for 68 countries and the EU and announced that they will come into force in a week.
Taiwan was awarded a tariff of 20 percent, which is higher than neighboring countries Japan and South Korea, which received 15 percent.
However, according to Trump, the important export of semiconductors and microchips for Taiwan and South Korea may be subject to other specific tariffs, the scope of which is still unclear.
