The index that measures the dollar against peer currencies hit its lowest since March 9. The dollar index has lost nearly 8% since its March 20 peak, when a global dollar funding crunch saw a surge in demand. It is down 1.5% year-to-date.
U.S.-China ties have deteriorated this year over issues ranging from the new coronavirus and telecoms-gear maker Huawei, to China's territorial claims in the South China Sea and Hong Kong crackdown.
The U.S. State Department said the Chinese mission in Houston was being closed "to protect American intellectual property and Americans' private information."
Chinese state media said on Thursday the move was a political ploy ahead of November presidential elections, and one source with knowledge of the matter told Reuters China was considering closing the U.S. consulate in Wuhan in response.
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"If China does limit its retaliation to closing the Wuhan consulate, the market will probably take it in stride, but if China instead decides to do something that escalates the tensions between the two countries, we could quickly switch to a 'risk-off' mood," said Marshall Gittler, head of investment research at BDSwiss Group.
Against the safe haven Japanese yen, the dollar was flat at 107.15.
The euro was at US$ 1.1573, just below a 21-month high of US$ 1.1601 hit earlier this week after Europe's leaders agreed a recovery fund.
The Australian dollar retreated from a 15-month peak to around US$ 0.7151, while the kiwi was just below Wednesday's six-month top of US$ 0.6678.