Tuesday's early European trading hours saw the greenback stabilize, while the Australian dollar fell as a result of the Reserve Bank's decision to hold interest rates constant at its most recent policy-setting meeting.

The dollar index that gauges the greenback versus its major pairs shifted slightly lower to 102.612. Holiday-related tight ranges for the dollar

Given that U.S. markets will be closed on Tuesday in observance of Independence Day and that the week will end with important employment data that could affect the Federal Reserve's next move, the dollar is likely to trade in narrow ranges.

EUR/USD steadied at 1.0910, Germany's manufacturing powerhouse faces a challenging trading environment even as exports decreased in May.

GBP/USD advanced by 0.1% to 1.2705, considering that the country's inflation rate stayed at 8.7% in May, the highest of any significant advanced economy, the Bank of England is also expected to keep raising interest rates.

USD/JPY slipped 0.2% to 144.39, with markets continuing to keep an eye out for any prospective government intervention in currency markets, the yen was trading at seven-month lows.