The New Zealand dollar was at 65.51 US cents from 65.59 this morning, while the trade-weighted index was at 72.06 points from 72.13.
The Australian data showed the unemployment rate rose to 5.2 per cent in March from 5 per cent in February. But there were 28,400 new jobs created, roughly twice the number expected.
The market had been looking to weakness in the data to justify the Reserve Bank of Australia cutting its cash rate.
"The Aussie data was, on face value, weak and there was a downward reaction in the Aussie," says Imre Speizer, strategist at Westpac.
"Then the analysts opined that, when you look under the bonnet, it was neither weak nor strong, so it didn't really add to the case for an Aussie rate cut," Speizer says.
Within an hour the Australian dollar was back to trading about where it was before the data, he says.
The market remains attuned to further risk of escalation in the ongoing US-China trade war.
The latest move is that the US has added Chinese firm Huawei to its "entity list," a move known as the corporate equivalent of the death penalty because it makes it virtually impossible for companies on the list to survive once US firms are discouraged from doing business with them.
The US Commerce Department reached its decision as Huawei "is engaged in activities that are contrary to US national security or foreign policy interests."
Local phone company Spark had wanted to use kit from Huawei, the world's largest telecommunications equipment maker, to build its 5G network but the Government Communications Security Bureau vetoed that on national security grounds.
Earlier today, the Commerce Commission said in a draft report that excluding Huawei from the 5G build risks driving up costs and undermining competition.
The New Zealand dollar was trading at 4.5048 Chinese yuan from 4.5088, at 50.97 British pence from 51.06, at 58.42 euro cents from 58.53, and at 71.69 Japanese yen from 71.84.
The New Zealand two-year swap rate fell to 1.5397 per cent from 1.5665 yesterday, while the 10-year swap rate eased to 2.0600 per cent from 2.0875.