Inflation data released earlier largely met expectations though the numbers were soft enough to prompt some investors to speculate the Fed will keep stimulus measures such as its monthly USD85 billion bond-buying program in place for a while, which ultimately softened the greenback.
Stimulus programs weaken the currency to spur recovery.
In U.S. trading on Tuesday, EUR/USD was up 0.30% at 1.3406.
The Labor Department said earlier that the country's consumer price index in May rose 1.4% on year, in line with forecasts and up from 1.1% in April though below the Fed's 2.0% target.
Consumer prices rose 0.1% in May from April, slightly below expectations for a 0.2% increase.
Core inflation, which excludes food and energy costs, rose 0.2% in May from April, also in line with expectations.
The year-on-year core inflation rate came in unchanged at 1.7%
In a separate report, the Commerce Department said the number of building permits issued in the U.S. fell 3.1% in May to 974,000, outpacing expectations for a decline of 2.8% to 975,000 units, which gave the euro room to rise.
U.S. housing starts rose by 6.8% last month to hit 914,000 units, below expectations for an increase of 11.4% to 950,000.
In the eurozone, the ZEW index of German economic sentiment rose to 38.5 in June from 36.4 in May, beating analysts' calls for the index to rise to 38.1.
The report said the German economy is likely to slowly pick up speed in the second half of this year, which strengthened the euro against the dollar.
Investors largely ignored comments by European Central Bank President Mario Draghi, who said the eurozone's monetary authority stood ready to use interest rates and non-standard measures to shore up growth in the currency bloc's economy.
The greenback, meanwhile, was up against the pound, with GBP/USDtrading down 0.47% at 1.5647.
The Office for National Statistics said the U.K. consumer price index rose 2.7% in May, above expectations for a 2.6% increase and up from a seven-month low of 2.4% in April.
Core CPI rose 2.2% up from 2% in April.
Consumer prices rose 0.2% from a month earlier, compared to expectations for a 0.1% increase, after rising 0.2% in April, though Fed uncertainty kept Cable lower.
The dollar was up against the yen, with USD/JPY up 0.80% at 95.26, and down against the Swiss franc, with USD/CHF trading down 0.35% at 0.9194.
The dollar was mixed against its cousins in Canada, Australia and New Zealand, with USD/CAD up 0.20% at 1.0207, AUD/USD down 0.56% at 0.9488 and NZD/USD trading up 0.09% at 0.8002.
The dollar index, which tracks the performance of the greenback versus a basket of six other major currencies, was down 0.07% at 80.76.
On Wednesday, all eyes will focus on the Federal Reserve and its announcement on monetary policy.
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