Australia

Australia's S&P/ASX 200 is on track for a soft open as investors continue to digest the implications of the Reserve Bank's decision to hold interest rates.

ASX futures are down by 0.2%, with no lead from U.S. markets, which were closed for the Independence Day holiday.

U.S. stock futures edged down ahead of a stretch of key economic releases, while European and Chinese stocks crept higher in a quiet trading session.

Oil prices continued to climb, which could offer further support to Australian energy stocks. Energy was the best-performing sector Tuesday as the ASX 200 rose 0.45%.

Financial and real-estate stocks also rose as the RBA decided against raising the cash rate.

Turning to commodities, gold is flat at US$1,925.29 per troy ounce. The Brent Crude has risen 2.4% to US$76.25 a barrel.

Meanwhile, the Australian dollar largely held flat at 66.93 US cents as The Wall Street Journal Dollar Index, which tracks the US dollar against 16 other currencies, edged up to 103.11.

Australian government 2- and 10-year bonds currently yield 4.07% and 4.01%, respectively.

Asia

Chinese shares ended higher, reversing morning losses amid gains from auto and chip stocks.

In focus is the impact of Beijing setting export restrictions on some minerals used in chipmaking Monday night, in a potential escalation of the tech trade rivalry between the two countries.

The benchmark Shanghai Composite Index ended flat at 3245.35. The Shenzhen Composite Index rose 0.4%, and the tech-heavy ChiNext Price Index added 0.2%.

Hong Kong stocks ended the session higher, extending a recovery trend to a third session after having weakened significantly since mid-June.

The benchmark Hang Seng Index rose 0.6% to settle at 19415.68. Drugmakers, biotech stocks and digital healthcare companies led the gains. Hansoh Pharmaceutical surged 6.6%, sustaining a recent rally as investor optimism got a boost from the company securing regulatory approval for a new innovative drug.

Treasury Secretary Janet Yellen is due to travel to China on Thursday to meet with senior government officials.

Singapore's FTSE Straits Times Index edged 0.1% lower to close at 3203.77. While China's move to restrict exports of chip-making minerals to the U.S. raises prospects of more tit-for-tat escalation between them, tensions still appear measured for now as both countries are seeking to deal with their respective economic issues, said Yeap Jun Rong, market analyst at IG, in an email.

Europe

U.K. bank shares fell after a report claimed financial regulators had requested a meeting with them to discuss profiteering concerns.

The Financial Conduct Authority is due to meet executives of some of the country's biggest banks Thursday to discuss concerns that interest paid on savings is falling behind rising mortgage rates, the Financial Times reports, citing unidentified sources.

"Banks have slipped back as they come under pressure to raise savings rates at the same speed that they increase their lending rates," CMC Markets analyst Michael Hewson writes.

"This has been a common refrain and something that the major banks have always been prone to--quick to cut rates on savings and slow to raise them. NatWest, Barclays and Lloyds are all lower."

North America

In North America, the market remained closed for Independence Day celebrations.