The total number of people with jobs rose by 37,700 - double the number economists expected.
This week, RBA governor Glenn Stevens, in a speech delivered in New York, said governments around the world were putting too much weight on monetary policy, raising questions about whether the RBA's easing bias would be enough to revitalise the economy.
All three events together meant the prospects of a rate cut from the RBA on May 5 had become less certain, said Sam Tuck, senior foreign exchange strategist at ANZ Bank.
He said the odds of a cut were now more like 50/50 from 70/30 previously.
But with the cross rate still within striking distance, parity could not be ruled out, he said.
The New Zealand dollar has gained ground in recent days against the US dollar, which has tended to put upward pressure on the NZ/Australian dollar cross rate.
If the flow of data out of the United States continued to point to weakness in the US economy, the kiwi could gain more ground, putting more pressure on the cross rate, he said.
Westpac said the cross rate was likely to remain strong so long as Australia's sluggish economy kept the RBA considering further easing and while the Reserve Bank of New Zealand continued to stick with its 3.5 per cent official rate.
HSBC said that while yesterday's data showed inflation was slightly higher than expected, it remained well contained.
"With underlying inflation comfortably in the lower half of the RBA's 2-3 per cent target band, the door is open for them to consider cutting the cash rate again," HSBC said.
Aussie update
• Inflation rose by 0.2% in the first quarter - just above market expectations.
• Unemployment rate fell to 6.10% in March from 6.20% in February.
• Number of people with jobs rose by 37,700 - double economists' expectations.
