Survey data on Monday showed factories in the euro zone had their worst month for almost six years in March, while economic data in the United States offered more hope. That reinforced concerns that while both economies face a slowdown, the euro region looks set to come out worse.
Kit Juckes, a strategist at Societe Generale, said that while there was little correlation between the gap in the Purchasing Managers Index surveys in the euro zone and the United States, signs of weakness would test the single currency as it fell towards the bottom of its recent trading range.
"The market is bearish and short, the poor data are not unexpected, but even so, a break through $1.1150 would surely trigger short-term stops," he said.
The euro weakened as much as 0.2 percent to $1.1190, slightly above the $1.1176 level reached last month - the weakest since June 2017.
The dollar index, which measures the US currency against a basket of rival currencies, rose as much as 0.3 percent to 97.430, a three-week high, helped by a rally in US stocks on Monday and the more positive US data.
Australia's dollar shed more than 0.6 percent to $0.7065 . The Reserve Bank of Australia's stress on the "downside risks for the global growth environment" on Tuesday probably caused the selloff even as the central bank kept interest rates on hold, said Commerzbank analyst Esther Reichelt.
The Australian government downgraded its growth forecasts on Tuesday but said it expected the economy to extend its enviable recession-free run of growth into a third decade.
Reichelt said the Aussie should rebound, helped by optimism over crucial trading partner China.
Sterling dropped half a percent after lawmakers rejected four Brexit proposals, heightening Britain's uncertainty just 10 days before it is due to leave the European Union. The pound fell to $1.3025 before stabilising around $1.3050 and stood at 85.835 pence against the euro.
The safe-haven Swiss franc strengthened to below 1.12 per euro and near 2019 highs. It touched 1.1182 francs, not far from the 2019 highs of 1.1164 hit last week.
RBC Capital Markets strategist Adam Cole said he did not expect the franc to hold its gains because the Swiss National Bank remained "sensitive" to a stronger currency, particularly when it traded beyond 1.12 francs per euro.
The SNB will be "the last central bank in the developed world to tighten rates," he said, and that should weigh on the currency in the medium-term.
Cryptocurrencies surged. Bitcoin jumped 20 percent to touch $5,000, its highest since November. Analysts struggled to explain the buying spree.