Trump's announcement came on Monday, but it is still unclear what the agreement actually contains.
In Japan, the Nikkei 225 index is down 0.1 percent, while the broader Topix is down 0.3 percent.
South Korea's Kospi, on the other hand, rose 1.9 percent.
The Hong Kong-based Hang Seng is down 1.3 percent, while Shanghai is up 0.1 percent and Shenzhen is up 0.9 percent.
