Nov 3 (Reuters) - Australian shares fell on Thursday, tracking overnight Wall Street losses, after hawkish messaging from the U.S. Federal Reserve and a steep rate hike, while asset manager Perpetual rose more than 10% on rejecting a buyout bid.

The S&P/ASX 200 index fell about 2.2% to 6,836.7, as of 0030 GMT. The benchmark ended 0.1% higher on Wednesday.

Wall Street ended sharply lower overnight, as comments from Fed Chair Jerome Powell indicated the Fed was nowhere close to slowing down the pace of monetary tightening, after raising rates by 75 basis points for its fourth consecutive meeting.

Back in Sydney, heavyweight miners fell 3.4% despite rising iron ore prices. BHP Group, Rio Tinto and Fortescue Metals Group dropped between 2.8% and 3.4%.

Financials also dropped 1.6%, with all of the "Big Four" banks losing between 1.3% and 1.9%.

However, Perpetual was last up about 9%, becoming the second-biggest gainer on the benchmark index after it rejected a $1.07 bln buyout offer from a consortium of overseas and local private equity and funds management firms.

New Zealand-based dairy firm a2 Milk was the highest gainer after it got temporary approval to export infant milk formula to the United States.

Shares of grocer Woolworths Group fell as much as 3.3%, as sales at its main Australian supermarkets unit contracted. It also dragged the consumer sector index down 2.1%.

New Zealand's benchmark S&P/NZX 50 index was down 0.5% at 11,229.71. a2 Milk and its supplier Synlait Milk were the biggest gainers, rising 7.7% and 3.9%, respectively.

New Zealand's central bank governor said he was confident the central bank would get inflation under control. (Reporting by Rishav Chatterjee in Bengaluru; Editing by Rashmi Aich)