The U.S. dollar index, composed of the euro and five other currencies traded against the greenback, touched a high last seen May 27 and was last up 0.48 percent.
The euro, which had inched up briefly after Greek legislators signed off on tough bailout terms, was last down 0.63 percent against the dollar at $1.0876 as doubts grew about whether the deal with creditors will work.
The euro zone common currency had dipped under $1.09 and struck a low of $1.0854 last seen on May 27.
The dollar was ahead 0.27 percent against the yen at 124.10 yen and up 0.2 percent against sterling, which had rallied in recent days in part because UK officials have been hinting at raising interest rates.
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Currency investors, who are less worried about Greece exiting the euro zone and about China's stock market, are increasingly focused on economic fundamentals and interest rate outlooks, according to analysts.
"Now that Greece is 'somewhat' resolved, the argument has shifted back to monetary policy divergence between the euro zone, UK and U.S.," said Tobias Davis, corporate hedging manager with Western Union in London.
He pointed to rises in the cost of dollar two-month forward swaps for euros as evidence of firming expectations that U.S. rates are heading higher.
Weak New Zealand inflation numbers added to pressure from a closely watched auction that showed global dairy prices tumbled to a 12-1/2-year low, pushing the New Zealand dollar as low as $0.6498, its lowest since 2009.