On Monday, the dollar generally rose against the basket of major currencies as the recent comments of the head of the Federal Reserve Janet Yellen to support the dollar.
Trading volumes are likely to remain reduced today as the markets in the UK, US and Germany are closed due to holidays.
Demand for the dollar strengthened after the Fed chief Janet Yellen said on Friday that interest rates willbe raised later this year. Yellen added that afterwards, in the next few years, the rate hike will be small and gradual.
The USD index, which tracks the US currency against the basket of six major rival currencies, rose 0.28% to 96.52.
The EUR/USD fell 0.42%, getting to 1.0966.
The European currency strengthened after European Central Bank President, Mario Draghi, said on Thursday at a conference in Portugal that the policy of the ECB helped to restore the economy of the eurozone.
Meanwhile, fears over a possible Greek default continues to prevail among market sentiments, as talks between the leaders of the Greek, French and German governments, which took place late last week ended with no signs of a breakthrough to unlock bailout funds.
The pound is stable; the pair GBP/USD is traded at 1.5489.
The dollar also changed a little against the yen and Swiss franc, with USD/JPY being at 121.63, and the pair USD/CHF at 0.9436.
The dollar against the yen rose to a two-month high after the publication of the report on inflation in the United States, surpassed analysts' forecasts.
The dollar rose by 0.07% to 121.62 yen, reaching 121.78 yen earlier. The rise above 122.04 will get the dollar to an eight-year peak against the yen.
Basic consumer price inflation in the US in April rose 0.3%, which was the highest growth since January 2013. The increase in inflation gives the Fed a reason to raise interest rates this year.
Australian dollar stays unchanged; AUD/USD was traded at 0.7827 and the pair NZD/USD fell by 0.08% to 0.7306.
The pair USD/CAD added 0.14% to 1.2297.