The euro edged down from a three-week high on Tuesday and European shares opened lower after the region's finance ministers rejected an offer by private creditors to restructure their Greek debt, raising the spectre of a messy default.

The ministers said they could not accept a coupon of 4 percent on new, longer-dated debt expected be issued to Greece's private creditors in exchange for their agreement to write down the nominal value of the debt they hold by 50 percent.

I think a deal will eventually be reached on Greece and for euro/dollar this has largely been priced in, Lauren Rosborough, senior currency strategist at Societe Generale said.

The euro slipped in early trade but only by around 0.05 percent from its closing level in New York to $1.3022. It remains well above a 17-month trough near $1.2624 hit on January 13, though off the three-week peak around $1.3050 hit on Monday.

The single currency had hit a low of $1.2990 in the previous session as investors turned their attention to Portugal, the next weakest euro zone member, whose bond yields have been rising steadily over the past week.

I wouldn't want to discount a further rally from here but in the medium-term our core view remains for euro/dollar to fall back to $1.17 by mid-year, Rosborough said.

Safe haven German government bonds also moved up from one-month lows with Bund futures around 20 ticks higher on the day at 137.64, and off one-month lows of 137.25 seen on Monday. Benchmark 10-year yields were about 1.7 basis points lower at 1.96 percent.

In equity markets, economic outlook worries added to selling pressure after German conglomerate Siemens, a bellwether for Europe's manufacturing industry, reported a 23 percent decline in its first-quarter core operating profit, missing the most pessimistic analysts' forecasts.

The pan-European FTSEurofirst 300 index of top shares, which notched a fifth straight week of gains last week, opened down 0.7 percent at 1,040.97 points.

The MSCI world equity index was down about 0.2 percent after another quiet day in Asia where many markets are still closed for the Lunar New Year holiday.

Sentiment may be further dented later in the day with the release of Markit's flash Eurozone Composite Purchasing Managers' Index (PMI), a measure of euro zone company activity.

The reports are expected to reflect deteriorating growth. A Reuters poll last week showed most economists believed the euro zone would wallow in a mild recession until the second half of this year, assuming the region's debt crisis does not flare out of control.

Risks posed by Europe's debt woes prompted the Bank of Japan to cut its growth forecasts on Tuesday.

(Additional reporting by Neal Armstrong; Editing by Catherine Evans)