"The FX market is generally taking its cue from overall risk sentiment and so equities are higher today," said Mark McCormick, currency strategist at Credit Agricole in New York. "Risk-sensitive currencies such as the Aussie dollar are higher as well."
Greece was still very much a concern for investors. Greek Prime Minister Alexis Tsipras was finalizing a tough package of tax hikes and pension reforms to send to euro zone authorities by midnight in a race to secure agreement at the weekend on a third financial rescue for his country.
European officials are now inclined to allow Greece to restructure its debt.
In late New York trading, the dollar was up 0.5 percent against the yen at 121.32. The greenback also rose against the Swiss franc, up 0.29 percent at 0.9479 franc.
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The euro, meanwhile, was down 0.46 percent against the dollar at $1.1024 having topped $1.11 in Asian trade.
"Signs that the EMU (European Monetary Union) could be broken up will likely lend itself into a surge in downside pressure on the euro," said Jane Foley, senior FX strategist, at Rabobank in London.
"That said, any sign that the system will remain coherent in the absence of its weakest link could then lend support."
A fall in U.S. yields, meanwhile, following the release of minutes of the Federal Reserve's June meeting offered little hope to dollar bulls. The dollar index though was up 0.23 percent at 96.52.
The dollar slipped after U.S. initial jobless claims rose last week to their highest since February. Initial claims for state unemployment benefits rose 15,000 to a seasonally adjusted 297,000 for the week that ended July 4, the U.S. Department of Labor said on Thursday.