The euro advanced across the board on optimism Greece was making progress in efforts to secure funding and stay in the euro zone.
The safe-haven yen and Swiss franc fell on Thursday after Chinese stocks rebounded.
The yen rose to a seven-week high against the dollar on Wednesday, as investors bought the Japanese currency for safety.
The euro will dip if Greece leaves the euro zone, but a protracted downtrend is unlikely, FX strategist Jens Nordvig says.
The threat to the euro area from the Greek crisis and an increasing excess supply of the euro liquidity has driven the dollar up 20% against the euro.
The euro fell more than 1 percent against a buoyant U.S. dollar on Tuesday.
The euro slipped against a stronger dollar, falling over 1 percent after the European Central Bank toughened up on Greek banks.
The euro tumbled across the board, but was off its lows, after Greece voted to reject the conditions tied to the country's debt bailout deal.
The dollar stuck around as disappointing US jobs data and caution ahead of Greece's referendum on bailout conditions kept the market mood subdued.
The U.S. dollar slipped against a basket of major currencies on Thursday after U.S. jobs data lagged expectations.
The euro dipped, buffetted by a flurry of reports on new concessions made by Greece to its European creditors.
The euro was broadly lower as investors braced for the near certainty that Greece will default on a repayment to the IMF.
The euro proved broadly resilient to Greece's moving one step closer to an exit from the single currency.
The ongoing Greek debt talks left currency markets in tight ranges on Friday.
Ongoing Greek debt talks sidelined currency investors, demonstrating their unwillingness to take bold positions as deadlines for a deal come and go.
The dollar pared earlier losses on Wednesday after edging lower while U.S. 10-year Treasury yields dipped.
The U.S. dollar rose on Tuesday, underpinned by rising U.S. Treasury yields and prospects for interest rate increases.
The euro was mixed on Monday as a new cash-for-reforms offer from Greece raised hopes a tangible deal is taking shape.
The euro fell against other major currencies, weighed down by anxieties that Greece may soon default on debts.
The dollar declined, with weaker-than-forecast US consumer inflation data making traders even more uncertain about when the Fed will hike rates.