The Australian dollar is still sinking even though the country's reserve bank has intervened in the foreign exchange market for a third time since Friday.
The intervention has prompted speculation that the New Zealand Reserve Bank may intervene to support the local currency.
The New Zealand dollar lost four cents against the United States dollar over the weekend and 15% during the past week as investors pulled funds back to home markets.
The New Zealand Reserve Bank has said it hoped the fall would help boost exporters' earnings and the economy.
But there are signs the steep falls are hurting some businesses unprepared for such a significant drop against the greenback.
A fall in the currency could increase costs for some businesses as they struggle to get the benefits while working out existing currency hedging contracts.
The New Zealand Reserve Bank has $11 billion at its disposal to support the currency, but economists say it may hold off in the hope the slide will boost export earnings in the long run.
In Australia, traders continued to shun the local currency during another weak offshore session on Monday night.
The Australian dollar was down to US60.12 cents on Tuesday morning. The last time it was below US60 cents was in April 2003.
The Reserve Bank of Australia intervened in the foreign exchange market again on Tuesday morning to improve liquidity. It previously did so on Friday and Monday.
The bank previously bought Australian dollar reserves in August 2007 and in early 2001 when a recession in the United States helped push the Australian currency below US50c.