* Dollar groggy, USD index suffers biggest one-day fall overnight

* Lingering Greece debt hopes prop up euro

* Commodity currencies rally on crude oil surge

* Greenback fares better against yen as Tokyo shares surge (Adds details, quotes)

By Ian Chua and Shinichi Saoshiro

SYDNEY/TOKYO, Feb 4 (Reuters) – The dollar nursed broad losses on Wednesday, having suffered its biggest one-day fall in over a year as it came under pressure from many fronts amid oil-fuelled gains by commodity currencies.

Buyers snapped up commodity currencies as the oil market extended its recovery and copper prices also surged.

Elsewhere in the market, the euro recovered on hopes that Greece may yet secure a new debt deal.

The euro’s rally from Tuesday’s low of $ 1.1312 went as far as $ 1.1534. It last traded at $ 1.1470, well off an 11-year trough of $ 1.1098 set last week.

That contributed to a 0.9 percent slide in the dollar index , its biggest one-day fall since October, 2013. The index last traded at 93.758 after stooping to 93.25 overnight.

In a development that supported the battered euro, Greek Prime Minister Alexis Tsipras sought to reassure international partners that Athens did not want to create divisions in Europe with its call for a new debt accord and said he was open to listening to alternative proposals.

Yet, there was still plenty of uncertainty whether Tsipras will be successful, suggesting the rally in the euro was more about positioning rather than any change in fundamentals, traders said.

Commodity currencies remained in the spotlight with crude oil up about 19 percent over the past four sessions, while copper saw its biggest one-day gain since July 2013. Oil’s recovery helped spur a global rally in risk assets.

“It feels a little strange seeing crude oil and equities move in tandem, as higher oil under normal circumstances would slow economic growth. But we just have to go with the flow, and brace for ‘risk on’ when oil goes up,” said Bart Wakabayashi, head of forex at State Street in Tokyo.

“Currencies appear to be at the whim of the oil market. For now oil has become an indicator of risk appetite,” he said.

The Australian dollar hovered around 78 U.S. cents, staging an impressive turnaround from a slump to a six year trough of $ 0.7627.

The short-covering rally followed the Aussie’s slump on Tuesday, when the Reserve Bank of Australia (RBA) cut interest rates to a record low 2.25 percent.

The Canadian dollar jumped for a second session to two-week highs of C$ 1.2353 per U.S. dollar. It last traded at C$ 1.2428.

Sterling climbed to $ 1.5198, pulling further away from a near 19-month low of $ 1.4952 set last month. The British currency had posted its best session in nearly 10 months on Tuesday.

Against the yen, the dollar fared better as U.S. Treasury yields jumped and a rally by Tokyo shares lessened the allure of the safe-haven Japanese currency. The greenback was rose 0.3 percent to 117.95, having recovered from a low of 116.87.

Traders said the dollar’s recent rally to multi-year highs against the yen and euro could falter as doubts emerge over whether the Federal Reserve will raise interest rates this year.

“When most central banks across developed and emerging economies are in easing mode, the assumption that the Federal Reserve will raise rates this year is starting to look questionable,” said David Absolon, Investment Director at Heartwood Investment Management.

“For Fed policymakers, the external environment and the actions of other central banks are becoming increasingly hard to ignore,” he wrote in a note to clients.

(Editing by Shri Navaratnam and Simon Cameron-Moore)