The main S&P/ASX200 index was up 11.9 points, or 0.1 per cent, to 8868.4, and little changed from the open, as the broader All Ordinaries added 16.5 points, or 0.2 per cent, to 8993.7.
Most market sectors were in the green, with the materials and consumer sub-indices leading the way, while the banking and energy sectors carried most of the major loss-makers.
The Reserve Bank of Australia board will conclude its two-day meeting on monetary policy later on Tuesday, when it's expected to announce a 25 basis point rise in the cash interest rate to 4.85 per cent.
The widely expected result would be the fifth rate rise this year and would take the cash rate to its high level in about 18 years, or since the global financial crisis.
"In addition to the decision itself, a keen eye will be on the RBA's updated Statement on Monetary Policy and its latest inflation forecasts to gauge the odds of further rate hikes going forward," Capital.com senior market analyst Kyle Rodda said.
"Currently, futures markets imply an 80 per cent chance of a hike today and the non-trivial risk of another at the start of next year."
Commonwealth Bank has already cut its mid-2027 Australia economic growth to an annualised one per cent, from 1.8 per cent.
By noon, most of the major banks were lower, with Westpac off 1.2 per cent to $36.74, National Australia Bank down 0.2 per cent to $40.81 and ANZ falling 1.1 per cent to $40.09. But the nation's biggest mortgage lender Commonwealth Bank was 0.6 per cent higher at $166.10.
Among the big miners, BHP was broadly flat at $56.77, Rio Tinto was down 0.5 per cent to $144.83 and Fortescue was off 0.3 per cent to $14.23.
Elsewhere, supermarket giant Woolworths was up 0.4 per cent to $39.65 and Coles gained almost one per cent, to $21.48.
In the US overnight, the S&P 500 fell 0.5 per cent after erasing earlier gains while the Dow Jones Industrial Average rose 0.4 per cent and the Nasdaq composite fell 1.1 per cent as the market digested disappointing earnings results from Alphabet and Google.
But after the US close, Apple released better-than-expected fourth quarter results showing a 12 per cent rise in earnings to $US30.71 billion ($A43.88 billion).
"Apple has been a solid performer throughout 2026 as it has largely avoided the AI volatility and large capital expenditure of the hyperscaler tech companies," VanEck Australia's deputy head of investment Jamie Hanna said.
Meanwhile, Israel and Hamas have agreed to the first phase of US President Donald Trump's plan for Gaza, a ceasefire and hostage deal that could be a first step towards ending the Middle East war.
In the commodities market, Brent crude oil was trading lower at around $US104.77 a barrel on news of the Middle East developments while spot gold was higher at $US3965 ($A5,665) an ounce.
The Australian dollar was buying 70.03 US cents, down from 70.21 US cents at 5pm on Monday.
