* Energy stocks outperform ASX 200

* RBA does not see cash rate increasing until at least 2024

* NZX 50 traded flat

Sept 14 (Reuters) - Australian shares ended higher on Tuesday as oil stocks led the gains on firmer prices, while the country's central bank expressed near-term optimism on economic recovery and doused investor fears over sooner-than-expected interest rate hikes.

The S&P/ASX 200 index climbed 0.16% to close trade at 7,437.3 points. The benchmark ended 0.25% higher on Monday.

Reserve Bank of Australia (RBA) Governor Philip Lowe said on Tuesday he was confident economic activity would rebound quickly once coronavirus restrictions were eased in coming months and reiterated that interest rates were not expected to rise from record lows until 2024 given persistently sluggish wage growth.

"RBA Governor's latest speech lifted market sentiment to some extent and calmed investor concerns over sooner-than-anticipated interest rate hikes, a stance which is more forward-looking as it sees the setback to the economic expansion as temporary," Chief Executive Officer of Kalkine Group Kunal Sawhney said.

Australian energy stocks rose 4.45% after oil prices scaled a six-week high as U.S. output remains slow to return two weeks after Hurricane Ida slammed into the Gulf Coast and on worries another storm could affect output in Texas this week.

Heavyweights Beach Energy Ltd and Woodside Petroleum Ltd led gains in the sub-index as well as on the local bourse, advancing up to 7.7% and 6.7%, respectively.

Bucking the trend, supply-chain logistics specialist Brambles dived nearly 12%, marking its worst day in 4-1/2 years on higher investment spending plans.

Australian metals and mining index rose 0.52%, with heavyweights Rio Tinto and BHP shrugging off weakness in iron ore prices to gain more than 1% each.

Lithium miners Orocobre Ltd and Pilbara Minerals advanced up to 5.1% and 3.2%, respectively, as lithium prices hit three-year high as demand for electric vehicle batteries surges.

New Zealand's benchmark S&P/NZX 50 index traded flat to finish the session at 13,170.9 points.

(Reporting by Riya Sharma in Bengaluru; Editing by Sherry Jacob-Phillips)