THE dollar has opened marginally higher as the Cyprus bailout deadline approaches.

At 7am AEDT, the Aussie was trading at $US1.0438, up slightly from Friday's local close of $US1.0426.

During the weekend offshore session, the currency traded in a narrow range between a low of $US1.0422 and a high of $US1.0458.

The euro remained under pressure during overseas trading, as market players focused on the latest developments in Cyprus.

Cyprus faces the prospect of losing a 10 billion euro ($12.4bn) bailout package if the Mediterranean island nation cannot agree to terms with the European Central Bank.

While legislators in Cyprus rejected a proposed levy on all bank deposits last week, they were now considering a levy on all deposits more than 100,000 euros to raise the 5.8 billion euros required.