Greek Finance Minister Evangelos Venizelos said talks with private creditors on a bond swap deal that is key to the country avoiding an unruly default were "one formal step away".
The euro was also helped by a euro zone manufacturing purchasing managers' survey (PMI) which was revised up, with German factories posting growth, and by decent demand at auctions of German and Portuguese debt.
The euro was up 0.8 percent at $1.3184, off an earlier low of $1.3026 on EBS. Traders said it extended gains after pushing through stop loss orders at $1.3125 and $1.3150, moving it back towards Friday's six-week high of $1.3235.
"The euro is going to benefit today from this rebound in the PMIs ... If that is replicated by the ISM (US manufacturing data) this afternoon, that could well prolong this rebound," said Ian Stannard, head of European FX strategy at Morgan Stanley.
Athens must still convince international lenders it can push through spending cuts and labour reform while concerns grow that Portugal may follow in Greece's footsteps and be forced to restructure its debt.
"There would be an initial positive response from a PSI agreement ... but PSI is just one step along the way of being able to put the Greek package into place," said Morgan Stanley's Stannard.
Analysts said the euro would need to breach technical resistance at $1.3244, the 38.2 percent retracement of its October-January decline, for fresh upside momentum.
YEN INTERVENTION ALERT
Traders were on alert for possible Japanese intervention to stem the rise in the yen as the dollar fell to its lowest in three months versus the Japanese currency, particularly as the euro was still weak around the 100 yen level.
The dollar fell to 76.027 yen on the EBS trading platform, its lowest since Oct. 31 when it hit a post-World War Two record low of 75.311 yen and prompted massive yen-selling intervention by Japanese authorities.
The euro was up 0.6 percent at 100.25 yen, having earlier dropped to 99.25.
"We are approaching the lows seen before the last round of intervention so obviously there's a lot of tension. It's a very unpleasant situation for the Japanese authorities," said Niels Christensen, currency strategist at Nordea in Copenhagen.
The dollar looked poised to lose ground for a fifth straight day against the yen, pressured by last week's pledge by the Federal Reserve to keep interest rates near zero until late 2014 which pushed yields on US Treasuries down sharply. This has dented dollar/yen, which is particularly sensitive to changes in US borrowing costs.
Focus will now turn to US ADP employment data due later on Wednesday as well as ISM manufacturing data ahead of non-farm payrolls on Friday. If these come in on the weak side this could increase the chances of more quantitative easing and weigh further on the dollar, analysts said.
The dollar index was down 0.6 percent at 78.805, while markets watched for any moves from the Swiss National Bank as the euro traded near the floor it set at 1.20 Swiss francs.
China's Purchasing Managers' Index earlier showed the manufacturing sector expanded modestly, easing concerns about the global economy and helping lift the Australian dollar, which hit a three-month high in the European session of $1.0715.