The dollar rose during trading on Tuesday, but it remained near the highest level in 20 years, which was recorded in the previous session, while the euro returned above the parity level.
This comes with increasing speculation that the US Federal Reserve and the European Central Bank are preparing to pass significant increases in interest rates.
Both the US Federal Reserve and the European Central Bank are seeking to tighten their monetary policies to curb the highest level of inflation in decades.
In terms of trading, the dollar index rose 0.074 percent to 108.73 at 1900 GMT, after touching 109.48 on Monday, the highest level since September 2002.
Later this week, markets are awaiting US jobs data for August which will be released on Friday.
As for the euro, it rose by 0.28% to 1.0028 against the dollar, regaining its rise to the highest level of parity with the US currency.