
The yen strengthened 0.6% against the greenback to ¥158.68 per dollar.
The euro was up 0.7% at US$1.167, while the British pound appreciated 0.7% to US$1.3385.
The Australian dollar climbed 1.3% to US$0.7068 as its New Zealand counterpart jumped 1.4% to US$0.5810.
Trump had earlier threatened widespread attacks on Iran’s civilian infrastructure.
Markets turned risk-on after the announcement, less than two hours before his deadline for Tehran to reopen the Strait of Hormuz expired.
The US dollar index, which measures the greenback’s strength against a basket of six currencies, was down 1.0% at 98.97, a two-week low.
Cryptocurrencies also rallied, with Bitcoin advancing 3.4% to US$71,664.41, as Ether surged 5.7% to US$2,234.78.