The benchmark S&P/ASX200 index finished Friday up 16.6 points, or 0.23 per cent, to 7,154.8, while the broader All Ordinaries closed up 18.2 points, or 0.25 per cent, to 7,334.9.
But after losses every other day this week, the ASX200 finished the week down 1.71 per cent, its worst week since mid-March, amid the debt-ceiling stalemate.
But Reuters, Bloomberg and the New York Times were reporting on Friday that a deal was taking shape which would raise the debt ceiling for two years, with various provisions that would allow both Democrats and Republicans to claim some sort of victory.
Negotiators were beginning to draft the legislative text of an agreement, according to the Times, although some details were still up in the air.
AMP chief economist Shane Oliver warned there was still the potential for more setbacks and it could take a further share market fall - which would impact both global and Australian equities - to ensure a deal was passed by Congress.
"Agreeing too early would not go down too well with either sides' base – so a last minute deal with argy bargy along the way was always most likely," he wrote in an analysis.
A deal might result in a short-term bounce but over the next few months the market looks vulnerable, Mr Oliver added, pointing to banking stress, weakness in industrial commodities, soft leading economic indicators in the US and Australia and doubts about China's recovery.
"We remain of the view that shares will do okay on a 12-month view as central banks ease up as inflation cools but the next few months are likely to be rough," he said.
Tech was the ASX's best-performing sector on Friday, buoyed for a second day by enthusiasm over artificial intelligence after chipmaker Nvidia's rosy quarterly earnings report led to a 1.7 per cent overnight rally on the Nasdaq.
Tech companies collectively gained 1.6 per cent with printed circuitboard company Altium adding 3.6 per cent, NextDC growing 3.5 per cent and Appen climbing 1.2 per cent as new-ish chief executive Armughan Ahmad used an artificial intelligence chatbot to welcome investors to the AI training company's annual general meeting in Sydney.
Fisher & Paykel Healthcare was the worst performer among the ASX200, falling 6.3 per cent to a four-month low of $22.48 after the New Zealand respiratory products company announced a full-year profit of $NZ250m, down 34 per cent from last year and $5m under expectations.
"The second-half result was encouraging as market conditions progressed towards more of a normal state and both of our Hospital and Homecare product groups delivered good growth," managing director and chief executive officer Lewis Gradon said.
The heavyweight mining sector was up 0.9 per cent after five straight days of losses amid concerns about China's recovery.
BHP gained 1.4 per cent to $42.75, Fortescue Metals added 3.3 per cent to $19.62 and Rio Tinto climbed 2.3 per cent to 107.77.
All of the Big Four banks finished higher, with NAB the best performer, adding 0.7 per cent to $26.23.
ANZ and CBA both gained 0.5 per cent, to $23.47 and $98.16, respectively, while Westpac edged 0.1 per cent higher to $20.92.
Latitude Financial Group fell 3.5 per cent to a seven-week low of $1.25 after the personal finance company said it was unlikely to pay a half-year dividend and had set aside $46 million to pay for fallout from the massive hack of customer data from its systems in March.
Humm Group fell 8.2 per cent to 39c after its buy now, pay later subsidiary received an interim stop order from the securities regulator temporarily forbidding it from signing up new customers.
The Australian dollar was buying 65.22 US cents, from 65.34 US cents at Thursday's ASX close.
ON THE ASX:
* The benchmark S&P/ASX200 index finished Friday up 16.6 points, or 0.23 per cent, at 7,154.8.
* The broader All Ordinaries added 18.2 points, or 0.25 per cent, to 7,334.9.
CURRENCY SNAPSHOT:
One Australian dollar buys:
* 65.22 US cents, from 65.34 US cents at Thursday's ASX close
* 91.09 Japanese yen, from 91.09 Japanese yen
* 60.76 Euro cents, from 61.07 Euro cents
* 52.82 British pence, from 52.84 British pence
* 107.33 NZ cents, from 107.18 NZ cents
