Australian shares rose on Tuesday's close, tracking Wall Street markets, as investors cheered President Trump's decision to delay European Union tariffs.

The S&P/ASX 200 Index rose 0.56% or 46.6 points to close at 8,407.6.

European Commission President Ursula von der Leyen said trade talks can move ahead, but a "good" deal may take time, with Trump's tariff pause ending July 9.

"The stock market seems to dance to Trump's tune: first a threat, then a pullback, quickly followed by a rebound as speculative investors anticipate a concession from the US President," said Jochen Stanzl, chief market analyst at CMC Markets.

On the domestic front, Australian consumer confidence fell last week despite the recent rate cut by the country's central bank, according to a report from ANZ and Roy Morgan.

In company news, HealthCo Healthcare and Wellness REIT (ASX:HCW) and the Unlisted Healthcare Fund (UHF) said that two entities within tenant Healthscope have entered receivership and administration.

Woodside Energy Group's (ASX:WDS) AU$30 billion plan to extend its North West Shelf gas project beyond 2030 and up to 2070 faces fresh scrutiny after archaeologists linked industrial emissions to damage on ancient Aboriginal rock art at Western Australia's Burrup Peninsula.

ALS (ASX:ALQ) said it is launching a fully underwritten A$350 million institutional placement at an offer price of AU$16.70 per share.