The greenback, as tracked by the U.S. dollar index against a basket of currencies, has this week clocked a 1.5 percent rise, and was last up 0.18 percent on Friday. That would be the index's best showing since the week ended May 22.
The euro was off on Friday at $1.0841, a level last seen on May 27 and down more than 2 percent on the week as currency investors shifted attention from the Greek crisis to economic fundamentals that favor the United States. It last traded at $1.0849, down 0.22 percent.
"Part of the dollar recovery is because the clarity on Greece helps the euro come back in lower ... That gets the focus back on moving towards policy normalization," said Saxo bank's head of FX strategy, John Hardy.
Most traders and strategists reckon the diverging policy outlook between the euro zone and the United States should see the euro continue to weaken, with many betting that it will fall below $1 in the next year.
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"The focus is turning to the U.S. rate cycle, and (the market reckons) a September rate hike is still, if not probable, at least possible," RBC Capital Markets global head of FX strategy, Adam Cole, said. "From now the euro goes down primarily because the dollar is going up."
Sterling hit a 7-1/2-year high against the euro of 0.6992 pounds after Bank of England Governor Mark Carney gave his strongest hint yet on the timing of a UK rate rise, saying a decision would come into focus around the end of 2015.
The greenback was down 0.05 percent on the day against the yen at just above 124 yen after touching a one-month peak of 124.235 yen.