* Benchmark up for 7th straight session

* Energy stocks hit 3-month high

* Cenbank's policy not on preset path - Deputy Governor Bullock

* Woodside approves $7.2 billion Gulf of Mexico oil project

June 20 (Reuters) -

Australian shares rallied for the seventh consecutive session on Tuesday as investors bet that the Reserve Bank of Australia (RBA) could become less hawkish, after minutes of its latest policy meeting showed that a decision to hike interest rates in June was "finely balanced".

The S&P/ASX 200 index finished 0.9% higher at 7,357.80, its highest closing level since April 20.

In the minutes of the RBA's June meeting, the central bank said it was necessary to raise interest rates in June to ensure high inflation did not become embedded in wage and price expectations.

"There is a fair chance for the RBA to get less aggressive and even pause rates in July, given the statement today", said Henry Jennings, senior analyst and portfolio manager at Marcustoday Financial Newsletter.

Meanwhile, RBA's Deputy Governor Michelle Bullock upheld the central bank's policy direction, adding the policy is not on a preset path.

On the bourse, banking stocks hit a 7-week high, jumping 1.2%. The so-called "Big Four" banks advanced between 0.8% and 1.7%.

Miners reversed losses from Monday, rising 1%.

Energy stocks jumped 1.9% to hit their highest since March 8.

Sector major Woodside Energy rose 2.2% after it said it had approved the development of the $7.2 billion Trion ultra deepwater oil project in the Gulf of Mexico, its first major investment since its merger with BHP Group's petroleum arm last year.

Bucking the trend, gold stocks retreated 0.2% as gold prices were stuck in a relatively narrow range.

Lithium miner Lake Resources lost nearly 20% and was the top loser on the benchmark, a day after it announced a three-year production delay at its Kachi project in Argentina.

In New Zealand, the benchmark S&P/NZX 50 index rose 0.3% to 11,789.37.

The country said it would examine profitability of its banks and investigate whether competition in the sector was working well for consumers. (Reporting by Poonam Behura in Bengaluru; Editing by Nivedita Bhattacharjee)