The benchmark S&P/ASX200 index on Monday finished up 6.8 points, or 0.09 per cent, at 7,410.4.
The broader All Ordinaries gained 6.1 points, or 0.08 per cent, at 7,622.2.
The ASX200 closed out July up 2.88 per cent, its best performance since a 6.2 per cent gain in January.
In the US on Friday, the Commerce Department reported the Federal Reserve's preferred measure of inflation, the personal consumption expenditures price index, had shown further signs of cooling in June, falling to its lowest level in nearly two years.
"The data adds to the probability that the Federal Reserve can navigate a soft landing," said eToro market analyst Josh Gilbert.
Closer to home, the futures market was pricing in less than a 10 per cent chance of the Reserve Bank raising rates on Tuesday, following readouts last week showing inflation and retail sales dropping faster than expected.
Commentators were more mixed, with St George senior economist Jarek Kowcza among those forecasting a hike that would take the cash rate to 4.35 per cent.
"We concede it will be another close call and finely balanced decision," Mr Kowcza wrote.
"Ultimately, the board's interpretation of the balance of risks will determine which way the pendulum swings."
Eight of the ASX's 11 sectors finished higher on Monday, although the gains for all of them were mostly modest.
Health care was the most improved, rising 0.6 per cent, while consumer staples lost the most ground with a 0.8 per cent fall.
Woolworths fell 1.3 per cent to $38.62, Coles dropped 0.9 per cent to $18.19 and Endeavour Group dipped 0.3 per cent to $6.08.
The heavyweight mining sector gained 0.1 per cent, with BHP up 0.5 per cent to $46.01, Rio Tinto advancing 0.4 per cent to $117.07 and Fortescue Metals flat at $21.68.
Silver Lake Resources plunged 20.2 per cent to a four-year low of 89c after forecasting decreased gold production in 2023/24 at a possibly higher cost base as it pauses production at its Sugar Zone mine in Canada.
IGO fell 4.6 per cent to a two-month low of $13.80 after the lithium, nickel, copper and cobalt miner announced record fourth-quarter earnings but forecast underwhelming 2023/24 guidance.
Lynas gained 2.6 per cent to $6.73 after the largest rare earths miner outside China posted record quarterly concentrate production at its flagship Mount Weld mine in WA.
In financials, most of the Big Four banks finished higher, with Westpac up 0.3 per cent to $22.34, CBA up 0.2 per cent to $105.71 and NAB up 0.1 per cent to $28.42.
ANZ was the outlier, basically flat at $25.75.
In utilities, Origin Energy dropped 0.6 per cent to $8.47 after Australia's largest energy producer reported a decline in household use of electricity and a fall in gas sales
In health care, Starpharma plunged 32.3 per cent to a 14-year low of 22c after announcing its partner AstraZeneca had discontinued development of a cancer-fighting drug candidate that used Starpharm's dendrimer drug delivery technology.
"This is clearly not what Starpharma would have hoped for," said CEO Jackie Fairley, while noting the drug's issues did not involve Starpharma's dendrimer technology.
The Australian dollar has rebounded against its US counterpart, buying 66.89 US cents, from 66.28 US cents at Friday's ASX close.
ON THE ASX:
* The S&P/ASX200 index finished Monday up 6.8 points, or 0.09 per cent, at 7,410.4.
* The All Ordinaries gained 6.1 points, or 0.08 per cent, to 7,622.2.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 66.89 US cents, from 66.28 US cents at Friday's ASX close
* 95.02 Japanese yen, from 92.50 Japanese yen
* 60.75 Euro cents, from 60.50 Euro cents
* 52.03 British pence, from 51.86 pence
* 108.01 NZ cents, from 108.11 NZ cents.
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