The Australian dollar has rallied past $US1.04 amid growing hopes the US will avoid a ‘fiscal cliff’ of spending cuts and tax hikes which could send the country back into recession.

At 0700 AEDT on Tuesday, the currency was trading at $US1.0409, up from Friday’s close of $US1.0367.

Overnight, the currency reached a high of $US1.0419 after US President Barack Obama said he believed a budget deal will be reached between Democrats and Republicans.

The positive sentiment saw global stock markets rally, with London’s FTSE 100 up 2.36 per cent and Paris’ CAC 40 finishing 2.93 per cent higher.

Advertisement At 0700 AEDT New York’s Dow Jones Industrial Average was 1.32 per cent higher, while the S&P 500 was up 1.74 per cent.

But LTG Goldrock director Andrew Barnett said the Australian dollar’s rally was likely to be short-lived.

‘‘The market was always going to have a bit of a dead-cat bounce following the sell-off last week,’’ he said.

‘‘But I’d be careful buying into this rally, purely because nothing has been resolved with the fiscal cliff,’’ he said.

Mr Barnett said the major local event for the Australian dollar on Tuesday would be the release of minutes from the Reserve Bank of Australia’s (RBA) November board meeting and a speech by RBA Governor Glenn Stevens.