The Nikkei 225 index in Tokyo had climbed 1.1 percent by lunchtime, while the broader Topix index had increased 0.8 percent.
The Hang Seng index in Hong Kong was up 1.8 percent after a few hours of trading.
The composite indexes in Shanghai and Shenzhen had risen 0.9 and 1.4 percent, respectively.
Donald Trump claims that Iran and Israel have agreed on a ceasefire. But the two countries have not yet unequivocally confirmed that this is actually the case.
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