The S&P/ASX 200 index rose 0.4 percent or 23.4 points to finish the day at 5575.90, after Beijing said a road map was discussed with U.S. officials for the next stage of trade talks between the world's top two economies.
Shares in China, Australia's biggest trading partner, made modest gains on the news as markets looked for progress in resolving the bitter trade dispute.
The Australian benchmark had fallen 2.3 percent on Monday, as investors worried last week's arrest by Canadian officials of a senior executive of Chinese tech giant Huawei for extradition to the United States could inflame fresh tensions between Washington and Beijing.
Global growth anxiety and slowdown in corporate earnings also undermined Australian shares, which have lost more than 10 percent so far this quarter, and are on course for their steepest decline since the quarter ending September 2011.
On the day, battered healthcare shares closed 1.6 percent higher to top index performers.
Medical equipment firm Resmed Inc led gainers, hitting a more than two-month high, after brokerage BMO upgraded the company's NYSE-listed stock and raised target price.
The financial index struggled through the session before ending marginally higher, with the country's 'Big Four' lenders all paring the day's losses to close higher.
Meanwhile, metals and mining stocks put on 0.6 percent after London base metals recouped some of previous session's losses, lifted by a weaker dollar.
Mining majors BHP Group and Rio Tinto both rose around 1 percent.
The Australian energy index slipped 0.3 percent, as most oil-related stocks continued to trade lower, even after global oil prices clawed back some of their losses towards the end of the day.
Oil and gas producer Oil Search Ltd fell 1.4 percent to a near 2 week low, while WorleyParsons Ltd pared losses to close 0.3 percent higher.
New Zealand's benchmark S&P/NZX 50 index rose 0.2 percent to finish the session at 8680.98, bouncing back from Monday's losses.
Fast-food group Restaurant Brands New Zealand Ltd, which closed 2.5 percent higher was among top gainers, after inking a deal to expand "Tex-Mex" food chain Taco Bell's brand in New Zealand and in Australia's New South Wales.