* NZ shares hits lowest level since March 27

* Fonterra at highest level in nearly two weeks

* Australia markets closed for public holiday

June 12 (Reuters) - New Zealand shares fell for a fourth straight session to finish at an over two-month low as caution prevailed ahead of the U.S. Federal Reserve's policy meeting later in the week, while markets in Australia were closed for a public holiday.

New Zealand's benchmark S&P/NZX 50 index retreated 0.6% to 11,615.55 points, their lowest level since March 27.

The Fed's rate hike decision is due on June 14, with markets pricing in a 73% chance that the U.S. central bank will keep rates steady in a range of 5%-5.25%.

Investors also await the U.S. inflation data for May, due Tuesday, which will likely influence the Fed's upcoming policy decision.

The trajectory of interest rates in the United States will have an impact on the economic activity of New Zealand, said Christina Leung, Principal Economist at the New Zealand Institute of Economic Research.

"Concerns about the impact of higher interest rates on economic activity in New Zealand has heightened concerns about the profitability of businesses and hence weighed on share prices here."

In New Zealand, shares of dairy exporter Fonterra Co-operative Group rose 1.0% after it received initial orders from the High Court, approving its proposal to return about NZ$800 million ($489.76 million) of capital to shareholders and unit holders.

Shares of Auckland International Airport Ltd fell 2.9% after the Auckland Council voted to sell 7% of its 18.09% stake in the company on Friday.

Meanwhile, top trading partner China reported a worse-than-expected 4.6% drop in factory gate prices for May on Friday, their steepest decline in seven years, and fuelled concerns over its fragile economic recovery.

(Reporting by John Biju in Bengaluru; editing by Eileen Soreng)