Most emerging Asian stocks rose on Tuesday after Wall Street rallied overnight, with the benchmark index in Taiwan hitting yet another record high, while currencies struggled for direction against a slightly firmer greenback.

Shares in Taipei rose as much as 1.3% to hit an all-time high of 22,787.67 points, while those in Seoul, Kuala Lumpur and Singapore rose between 0.1% and 0.8%.

Global investors are looking to a slew of speakers from the Federal Reserve for more clues on the Fed’s rate-cutting trajectory, following last week's decision to stay pat on policy.

The U.S. central bank has now pushed the beginning of its rate-cut cycle to December, which could mean that its Asian counterparts will have to exercise discretion while easing their own policy stances.

Futures now point to roughly 45 basis points worth of Fed cuts priced in for the rest of 2024.

At 0405 GMT, the dollar index, which measures the strength of the greenback against six major rivals, rose a tad to 105.39.

Among emerging Asian currencies, the South Korean won and the Taiwan dollar were largely unmoved, while the Malaysian ringgit and Philippines peso inched slightly higher.

Meanwhile, in Thailand, the baht was flat, even as stocks rose, as investors awaited decisions to crucial court cases - including those involving the current prime minister Srettha Thavisin and the former PM Thaksin Shinawatra.

These high profile cases could threaten to add to the political woes of the Southeast Asian country, in turn pressuring its financial markets.

The baht is currently the second worst-performing currency in Asia, having lost more than 7% on a year-to-date basis, while stocks are lingering near a four-year low.

"These political developments and uncertainty have weighed on THB (baht) in the near-term, and (are) leading to continued weakness in Thai risk assets and equity markets," analysts from MUFG said in a client note.

Markets in Indonesia were closed for a public holiday. The central bank is set to meet later this week to decide on its interest rates, in the wake of a depreciating rupiah.

Maybank analysts believe that the risk of a rate hike in its June 20 meeting has increased given the recent uptick in the USD/IDR pair, which is nearing a crucial level of 16,400.

(Reporting by Archishma Iyer in Bengaluru; Editing by Kim Coghill)