Despite fresh demands by U.S. President Donald Trump to cut interest rates, the Fed is expected to keep rates steady this time while laying the groundwork for a rate cut later this year.

"Mood in Asia will likely remain cautious with investors awaiting the Fed meeting and possible adjustments to the dot plots before taking on substantial bets," ING said in a note.

While weak economic data dragged Singapore's index lower in the previous session, expectations of a potential monetary easing in October lifted sentiment on Tuesday.

The city-state's main index rebounded to end nearly 1% firmer, hitting its highest close in more than a month.

"Singapore stocks are probably taking their cue from regional markets. The Hang Seng is trading higher as news about the protests over the weekend somewhat died down," said Liu Jinshu, director of research, NRA Capital.

"The U.S. markets have stayed near recent highs after a massive run upwards in the first week of June. This has also boosted confidence," he added.

In a technical rebound, Indonesian stocks snapped four sessions of declines to end stronger. Telekomunikasi Indonesia Tbk added 2.1% to the index, while Bank Negara Indonesia (Persero) Tbk closed 3.3% higher.

Malaysian stocks ended higher, with top percentage gainer Axiata Group rising 5.1%, while tourist resort operator Genting Malaysia closed up 1.5%.

Thai stocks clawed back from early losses to hit their highest close since October 2018, buoyed by gains in the energy sector.

PTT Public Company climbed 2.2%, while PTT Exploration and Production Public Co jumped to its highest close in nearly a month.

Bucking the trend, Vietnam's stocks closed 0.3% lower, dogged by consumer and real estate stocks.

(Reporting by Rashmi Ashok in Bengaluru, Editing by Sherry Jacob-Phillips)

By Rashmi Ashok