* New Hope Corp top gainer on the benchmark index

* Miners record best day in nearly two weeks

* Benchmark index marks best day in nearly two weeks

September 20 (Reuters) - Australian shares on Tuesday recorded their best day in nearly two weeks with broad-based gains following a late rally on Wall Street, while focus remained squarely on the upcoming U.S. Federal Reserve meeting.

The S&P/ASX 200 index ended 1.3% to 6,806.40 points. The benchmark fell 0.3% on Monday.

Markets have priced in a 75-basis-point increase at the end of the two-day meeting on Wednesday but are worried whether aggressive tightening by the Fed to tame stubbornly high inflation will tip the economy into a recession.

Boosting sentiment back home was the minutes of the Reserve Bank of Australia's (RBA) September meeting, which revealed that the central bank saw a case for slowing the pace of hikes as policy settings approached more normal levels.

"The market is probably factoring that future rate hikes will be smaller in size as the effect of the four back-to-back hikes of 50 bps will be felt with a lag," said Kunal Sawhney, CEO, Kalkine Media.

The energy index rose 2%, with gains led by New Hope Corp after the coal miner's shares hit a record high following a massive jump in its annual profit on soaring thermal coal prices. The mining index rose 2.8% even as China's strict zero-COVID policy and ailing property sector raised demand concerns. Rio Tinto, BHP Group advanced 2.5% and 3.6%, respectively, while Fortescue fell 0.9%.

"Despite a decline in iron ore prices, shares of iron ore miners rallied as easing lockdowns in the city of Chengdu and the government's efforts to stimulate the property sector in China continues to bode well for iron ore demand," he added.

The gold and financials indexes advanced 1.4% and 1.3%, respectively, with the Big Four banks gaining between 1.2% and 2%

New Zealand's benchmark S&P/NZX 50 index rose 0.3% to finish the session at 11,570.43 points. (Reporting by Tejaswi Marthi in Bengaluru)