May 16 (Reuters) - Australian shares rose for a second session on Thursday, pulled up by banks, tech and real estate stocks as cooling U.S. inflation data reignited investors' hopes for a September rate cut by the Federal Reserve, while investors digested local fresh jobs data.

The S&P/ASX 200 index rose 1.6% to 7,879.5 by 0135 GMT. The benchmark ended 0.4% higher on Wednesday.

April's U.S. consumer price index (CPI) data sparked hope among investors that inflation was cooling and that the Fed would lower its policy rate in September and December.

Markets are now pricing in a 72.4% chance of the Fed cutting interest rates in its September meeting, up from a 71.5% chance a month ago, according to the CME FedWatch Tool.

Meanwhile, data from the Australian Bureau of Statistics showed that net employment rose by 38,500 in April, higher than a Reuters poll of 23,700.

Back in Sydney, the rate-sensitive financials sub-index gained 1.3% with the "Big Four" banks advancing between 1.1% and 1.6%.

Real estate stocks gained 2.6%, with shares of Charter Hall Group and Goodman Group rising 4.2% and 3.6% respectively.

Technology stocks tracked their overseas peers higher, by advancing 2.4%. Shares of Xero and ASX-listed shares of Block rose 4.2% and 0.1%, respectively.

Healthcare sector gained 1.6% with shares of CSL and Ramsay Health Care recording a rise of 1.3% and 0.8%, respectively.

Mining stocks gained 0.9% on improving copper prices.

Mining behemoths BHP Group, Rio Tinto and Fortescue added between 0.6% and 1%.

Among other sectors, gold stocks rose 2.7%, with shares of Northern Star Resources up 3.4%.

Across the Tasman Sea, New Zealand's benchmark S&P/NZX 50 index rose 1.2% to 11,660.09 points.

Shares of New Zealand dairy giant Fonterra Co-operative gained 4.2% on planning a full or partial sale of its global consumer unit, its Fonterra Oceania unit and Sri Lankan business. (Reporting by Roshan Thomas in Bengaluru; Editing by Janane Venkatraman )