The SP/ASX 200 index closed up 5.0 points at a record 3,843.5, while the broader All Ordinaries index also hit a new all-time high, up 4.7 points at 3,854.5.
Singapore share prices closed 0.25 percent higher but a fall in index heavyweight Singapore Telecommunications (SingTel) after a government sale of stock in the company weighed on sentiment, dealers said.
The benchmark Straits Times Index rose 5.12 points to 2,015.77, while the broader All Singapore Equities index eased 0.22 points at 521.21.
Malaysian share prices closed flat as late profit-taking offset early gains made on the back of a strong rise on Wall Street and easing oil prices, dealers said.
Indian shares closed 1.0 percent higher on the back of a government decision to raise fuel prices which boosted sentiment in the oil refinery sector, dealers said.
The Bombay Stock Exchange's 30-share benchmark SENSEX index rose 58.48 points to close at 5,891.36.
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