The euro stabilized above support near $1.42, with gains accelerating after automatic buy orders were triggered above $1.4250.
It recouped some of Monday's losses, when fears mounted that Greece will have to restructure its debt possibly as early as summer.
The euro zone composite PMI, a broader measure of the private sector which combines the services and manufacturing data, nudged up to 57.8 from March's 57.6, data showed on Tuesday, beating forecasts for a fall to 57.1.
"The euro has found some support from firmer PMI data," said Vassili Serebriakov, currency strategist at Wells Fargo in New York.
"European debt concerns have moved to the sidelines but have by no means disappeared as evidenced by the recent spike in the cost of insuring against a Greek sovereign default."
The euro was last trading up 0.4 percent at $1.4290, after earlier rising as high as $1.4316 on Reuters data, well off a two-week low of $1.4155 reached on Monday.
Traders said the euro could encounter more selling ahead of the Easter holidays. It may also be hemmed in by options expiries due on Tuesday at $1.4200 and $1.4300.
The Canadian dollar firmed to a one-week high after data showed Canada's annual inflation rate in March jumped to its highest level since September 2008, ratcheting up pressure on the Bank of Canada to resume raising interest rates soon.
The U.S. dollar fell as low as C$0.9548 and last traded at C$0.9556, down 0.9 percent on the day.
GREECE RISK
Earlier, comments from a German Finance Ministry official that a Greek debt restructuring was inevitable caused the euro to pare some gains but it then rebounded.
Athens has denied such a possibility.
The comment supported an Athens newspaper report which cited a European Commission official saying Greece has accepted it cannot avoid a restructuring.
Analysts said the possibility that a country which has received a debt bailout may still have to restructure its borrowing was likely to encourage more investors to exit long euro positions.
"We are now seeing a rapid reversal of fortune with the euro now ranked as the overall weakest currency across the system of models," BNP Paribas said in an FX quantitative strategy note.
"With euro bearish signals still being generated we expect further euro selling over the short term."
Positioning data from the Commodity and Futures Trading Commission on Friday showed net euro long positions at their highest since December 2007, leaving scope for a reversal.
The U.S. dollar slipped 0.2 percent to 82.48 yen, while against a basket of currencies, it fell 0.4 percent to 75.202.
Standard & Poor's threatened on Monday to downgrade the United States' prized AAA credit rating unless the Obama administration and Congress find a way to slash the yawning federal budget deficit within two years.
Given that a majority of U.S. debt is owned by foreign investors, some analysts were surprised the S&P announcement failed to trigger lasting dollar selling.
"The price action suggests the euro was getting pretty tired," said Paul Mackel, director of currency strategy at HSBC.