"Today's figures and revisions to recent months paint a healthier picture of the labor market than expected," Riki Polygenis, co-heard of Australian economics at ANZ Research said in a note.
"It is unclear however, whether the gradual decline in the unemployment rate in the last couple of months suggest the beginning of a new downward trend; this is not our central case scenario given growth outcomes are expected to remain below trend, and retrenchments in the mining sector will continue," he said.
The Australian dollar jumped to 0.7770 against the U.S. dollar immediately after the decision from $0.7712 just before the data were released. Australia's benchmark S&P ASX 200 was little changed following the data, up 0.8 percent.
Earlier this month the Reserve Bank of Australia (RBA) surprised markets with its decision to keep interest rates on hold at 2.25 percent. Analysts expected the central bank to cut rates to a fresh record low amid tepid economic growth and as Australian dollar strength continues to exacerbate the rout in commodity prices despite its around 18 percent decline over the past 12 months.
Read MoreNew Zealand's top economic risk is Australia: PM Key
The RBA was likely waiting for more data on employment, inflation and property prices, analysts said following the policy decision. Thursday's employment data will likely prove integral to the central bank's next rate decision.
"For monetary policy, these stronger figures do lend support to the idea that there will be no further easing from the RBA following the expected cut in May," Polygenis added.
But even an interest rate cut in May appears less certain as the interbank market went from a 67 percent chance of a rate cut in May to 49 percent following the data, according to a tweet by IG analyst Evan Lucas.
"It is interesting that the market has set aside a May cut, especially after the RBA didn't move in April," Mitul Kotecha, head of FX strategy, Asia Pacific at Barclays told CNBC. "This [data] may change perspectives a little, but I don't think it will sway the RBA too much."
"In fact, the rally in the Aussie dollar may just push them even further into cutting rates when the RBA has been dissatisfied with the currency and they are more worried with currency strength now when commodity prices continue to drop," Kotecha added. "If anything, it might mean they do cut rates in May despite a strong report."