* Dollar hits nearly two-week low against euro

* Euro helped by short-covering, Greek government proposal

* Australian dollar, New Zealand dollar rebound

* Dollar gives back some gains against Swiss franc (Adds comments, updates prices)

By Sam Forgione

NEW YORK, Feb 3 (Reuters) – The dollar posted its worst day against major currencies since October 2013 on Tuesday on recent weakness in U.S. economic data and easing concerns surrounding Greece’s debt load, while a boost in risk appetite helped the Australian dollar recover losses.

The euro hit a nearly two-week high against the dollar at $ 1.15340. A spell of weaker U.S. data has dented confidence that the Federal Reserve will hike interest rates from rock-bottom levels by June, hurting the dollar and spurring many who had bet against the euro to “cover” their short bets by rapidly repurchasing the currency.

That trend was bolstered Tuesday, a day after Greece’s new government proposed plans for ending a standoff with its creditors, easing concerns of a Greek exit from the euro zone. The dollar index, which measures the greenback against a basket of six major currencies, fell nearly 1 percent on the day.

“It is pretty obviously just a big wave of short-covering that has fed on itself,” David Rodriguez, a quantitative strategist at DailyFX.com, a unit of retail FX broker FXCM (NYSE: FXCM – news) in New York, said of the euro’s rally.

The weakness in U.S. data continued Tuesday with a reading on new orders for U.S. factory goods falling sharply in December.

The euro, however, remained not far from an 11-year trough of $ 1.1098 touched on Jan. 26 following the European Central Bank’s launch of a landmark bond-buying program.

Relief over Greece, and a continued rally in oil prices, boosted risk appetite and drove traders to buy currencies that had sold off, including the Australian and New Zealand dollars. Both had hit multiyear lows earlier on Tuesday following a rate cut by the Reserve Bank of Australia.

The Australian dollar last traded mostly flat against the greenback after earlier hitting a nearly six-year low of $ 0.7627 . The New Zealand dollar reversed course from its lowest level in nearly four years to last trade up 1.15 percent at $ 0.7384.

“People are focusing on the risk story, and that’s I think supportive of currencies that have been pretty much beat up against the dollar,” said Mark McCormick, currency strategist at Credit Agricole (Swiss: ACA.SW – news) in New York.

The Swiss franc followed in the euro’s footsteps and gained modestly against the dollar after hitting a more than two-week low against the greenback on Monday.

The euro was last up 1.28 percent against the dollar at $ 1.14850. The dollar was last down 0.29 percent against the Swiss franc at 0.92470 franc. The dollar was down slightly against the yen at 117.485 yen. (Reporting by Sam Forgione; Additional reporting by Patrick Graham in London; Editing by James Dalgleish and Peter Galloway)