The benchmark S&P/ASX200 index on Tuesday finished down 3.9 points, or 0.04 per cent, to 8,947.5, while the broader All Ordinaries rose 3.1 points, or 0.03 per cent, to 9,177.2.
In Washington, President Donald Trump said he was "highly unlikely" to renew a two-week ceasefire with Iran due to expire at midnight GMT on Wednesday (10am Thursday, Sydney time).
"I'm not going to be rushed into making a bad deal," Mr Trump told Bloomberg News in a phone interview.
The US had turned back 27 ships trying to enter or exit Iran's ports since the US blockade of the Strait of Hormuz began a week ago, the US military said.
IG analyst Tony Sycamore said traders appeared to be balancing renewed geopolitical risks against persistent hopes that diplomacy could still deliver an extended or even permanent ceasefire deal.
Market participants would remain glued to every headline and the ceasefire expiration would provide some extra tension for Australian markets at 10am on Thursday, Mr Sycamore predicted.
Five of the ASX's 11 sectors finished lower on Tuesday and five finished higher, with telecommunications basically flat.
Energy was the biggest mover, dropping 0.8 per cent as Brent crude oil traded for $US94.67 a barrel, a tick less than on Monday.
Woodside fell 1.8 per cent, Santos dropped 1.5 per cent and Beach Energy retreated 2.5 per cent.
HUB24 was the biggest mover in the ASX200, dropping 8.3 per cent to a one-week low of $87.50 after the superannuation platform reported net inflows of $9 billion in the third quarter, up 22 per cent from a year ago.
Elsewhere in the financial sector, the big retail banks were mixed.
ANZ dropped 1.7 per cent to $37.28 and CBA dipped 0.3 per cent to $179.58, while NAB added 0.5 per cent to $41.21 and Westpac climbed 0.6 per cent to $40.25.
In the heavyweight mining sector, Rio Tinto grew 0.8 per cent to $173.86 after the mining giant reported that copper production was up nine per cent in the first quarter.
Rival BHP dipped 0.3 per cent to $55.51 while Fortescue was basically flat at $21.18 and South32 added 0.5 per cent to $4.41.
West African Resources dropped 0.6 per cent to $3.42 as its shares resumed trading following the partial nationalisation of one of its two main assets, the Kiaka goldmine in Burkina Faso.
The military junta that rules the West African nation will pay $175 million for an additional 25 per cent stake in the mine, far less than its market value.
The funds would be distributed to shareholders via a special dividend, the Perth-headquartered goldminer said.
Fellow goldminers Northern Star and Evolution were down 0.8 per cent and 1.6 per cent, respectively, as the precious metal traded for $US4,800 an ounce, down about $20 from Monday.
The Australian dollar was changing hands at 71.63 US cents, up from 71.56 US cents at 5pm on Monday.
ON THE ASX:
* The S&P/ASX200 dropped 3.9 points, or 0.04 per cent, to 8,949.4.
* The broader All Ordinaries gained 3.1 points, or 0.03 per cent, to 9,177.2.
One Australian dollar trades for:
* 71.63 US cents, from 71.56 US cents at 5pm AEST on Monday.
* 113.78 Japanese yen, from 113.68 Japanese yen.
* 60.84 euro cents, from 60.82 euro cents.
* 52.98 British pence, from 52.98 British pence.
* 121.15 NZ cents, from 121.81 NZ cents
