The ministers agreed to reconvene before the week is over, after Greece has thrashed out details with its international creditors the European Commission, the European Central Bank and the International Monetary Fund.
"Guarded optimism is driving the euro a little bit higher. There is clearly still a lot of uncertainty and officials in the euro zone have gone to considerable lengths to try to temper some of that optimism ahead of these meetings," said Omer Esiner, chief market analyst at Commonwealth Foreign Exchange in Washington.
"But the fact that we haven't seen any negative comments from finance ministers is generally a positive," he said.
In Afternoon New York trade, the euro was 0.25 percent lower at $1.1328.
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The euro rose 0.41 percent to 139.78 yen while dipping from its session high against the Swiss franc to trade up 0.24 percent at 1.0448 francs. The dollar rose 0.55 percent at 123.32 yen
Greek stock prices closed roughly 9 percent higher while 10-year Greek government debt yields dropped 134 basis points to 11.30 percent.
"Given the fact that the euro has been used as a hedge against other asset classes, European stocks, European bonds, I think we are seeing the euro recover a little bit given changes in market sentiment and market positioning, which is helping to provide a little bit of a bid for the euro in the short term," said Mark McCormick, currency strategist at Credit Agricole in New York.
"What we are looking to do is fade the euro rally. We'll probably see topside around $1.1450, but we don't think the outlook for Greece is really going to shift monetary policy or fundamentals more generally," McCormick said, expecting the euro will ultimately drop.