The moves, however, lacked the exuberance of the equities market as Sino-US tensions kept the mood in check.
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The moves, however, lacked the exuberance of the equities market as Sino-US tensions kept the mood in check.
The trade-sensitive Australian and New Zealand dollars each rose about 0.7pc, but remain below last week's highs.
The Norwegian crown also rose nearly 1pc versus the US dollar. The Chinese yuan, a barometer of US-China relations, was mostly left behind by a rally in other Asian currencies.
"At the moment the euro is torn between political risks on the one hand and positive sentiment on the markets as a result of further easing of the corona-related restrictions on the other. This morning, the latter is dominating, allowing it to appreciate against the dollar," said Thu Lan Nguyen, a currency analyst at Commerzbank.
"However, in view of the continued disagreements within the EU about a corona recovery fund, the single currency is likely to run out of steam quite quickly in euro-dollar," she said.
The euro was last up 0.4pc at $1.0935, while the dollar was down by 0.2pc against a basket of currencies at 99.50.
The mood among German exporters recovered somewhat in May after a "catastrophic" April, the first full month of coronavirus lockdown measures in Europe's largest economy, the Ifo institute said on Tuesday.
Japan ended its state of emergency on Monday, while Britain said it will reopen thousands of shops, department stores and shopping centres next month.
Versus the Japanese yen, the dollar rose 0.2pc to 107.89.
"Investors remain in risk-seeking mode, encouraged by ongoing progress in suppressing COVID-19, which is allowing the gradual reopening of economies," said Lee Hardman, currency strategist at MUFG.
"At the same time, the unprecedented amount of monetary and fiscal stimulus that has been put in place in recent months is providing support for risk assets," Hardman said.
The Australian dollar was up 0.8pc at 0.6590, still below its 0.6616 high from last week.
The New Zealand dollar rose 0.7pc to 0.6145. The Norwegian crown jumped 1pc versus the US currency to hit 9.9560.
Sterling traded at $1.2261, up 0.6pc on the day versus the US dollar. Against the euro, the recovery was more moderate, up 0.2pc at 89.19 pence.
The Chinese yuan was last trading flat in the offshore market at 7.1435.