The euro rose to as high as $1.3010, its highest level since late October, before easing to $1.2981, down 0.1 percent from late US trade on Monday.

"It was not a huge reaction because (the deal) was already priced in," said Joseph Capurso, a strategist at Commonwealth Bank of Australia.

He said the euro should start losing momentum and ease around a cent by the end of the week.

"Economic data in Europe is getting worse and you also have the unresolved US fiscal cliff in the background," he added.

Euro zone finance ministers and the International Monetary Fund agreed on a package of measures to reduce Greek debt by 40 billion euros, cutting it to 124 percent of gross domestic product by 2020.

Eurogroup Chairman Jean-Claude Juncker said ministers would formally approve the release of a major aid instalment needed to recapitalise Greece's teetering banks and enable the government to pay wages, pensions and suppliers on Dec. 13.

The euro had already pushed higher against the dollar over the past week, supported by hopes for a deal on Greece and also as investor risk appetite improved due to optimism that US lawmakers will reach an agreement to avoid the "fiscal cliff" of tax increases and spending cuts due to take effect next year.

Republicans and Democrats were still at odds, however, as Congress returned from its Thanksgiving holiday break.