July 28 (Reuters) - Australian shares gave up early gains to close lower on Tuesday as a rise in coronavirus cases stoked concerns of a stricter lockdown, while data showed employment was hit due to restrictions placed earlier.

The S&P/ASX 200 index fell 0.39% to 6,020.50 points at the close of trade.

The state of Victoria reported six deaths and 384 new cases in the last 24 hours, a day after posting a record surge in cases that prompted authorities to warn of an extension to the six-week lockdown already in place.

The economic pain of the lockdown was already evident as data on Tuesday showed the country's employment fell 1.1% between mid-June and mid-July.

"The choppiness we've been seeing in price action might be a reflection of the uncertainty as to whether lockdowns will be tightened, especially in Victoria and New South Wales," said Kyle Rodda, an analyst with IG Markets.

"Especially if you look at the Victoria situation, it's looking like we're staring down the barrel now with the extended lockdown, which will be a drag on growth."

The energy subindex lost over 1%, with Santos Ltd and Worley Ltd down 1.5% and 3.3%, respectively.

Gold stocks also fell 1%, with Northern Star and Ramelius Resources declining 1.2% and 5.2%, respectively.

Mining stocks rose, helped by robust iron ore prices. Global miner Rio Tinto and BHP Group advanced 1.2% and 1.9%, respectively.

Rio Tinto Ltd on Tuesday indicated the potential for a major new copper and gold mine in Western Australia after it discovered gold-rich deposits at its Winu project in the state.

Property manager Waypoint REIT was among the top losers on the benchmark after its largest shareholder sold its stake in the company.

New Zealand's benchmark S&P/NZX 50 index ended 0.6% lower to finish the session at 11,578.2. (Reporting by Soumyajit Saha in Bengaluru; Editing by Vinay Dwivedi)