* Malaysian markets among top gainers after long weekend * Investors torn between higher returns and the Fed"s stance - analyst * Singapore finance minister says will change tax system as needed June 8 (Reuters) - Asia"s emerging market currencies largely held steady on Tuesday, as traders adopted a cautious approach ahead of U.S. inflation data this week for clues on the Federal Reserve"s tapering timeline. Stock markets, on the other hand, were a mixed bag with Indonesian shares falling 0.8% on concerns over a spike in COVID-19 cases in some parts of the country, while Malaysian and Philippine shares rose around 0.5%. Malaysian markets were closed on Monday for a public holiday. Investors are keeping a close watch on U.S. inflation data due on Thursday, following on from last week"s payrolls report which tempered expectations of any near-term moves by the Fed to tighten policy. "There is some respite for EM assets as taper fears get pushed back," Eugene Leow, a rates strategist at DBS, said in a note. "We reckon investors are still torn between chasing higher returns while keeping an eye on when the Fed"s stance would change. An uncomfortable carry environment is likely ongoing as complacency on low USD rates seep in." The ringgit advanced 0.2%, while the Philippine peso and South Korean won weakened. The rupiah, favoured by foreign investors looking at Indonesia"s high-yielding debt, held steady even as stocks dropped. Bank Indonesia data showed foreign exchange reserves fell by $2.4 billion in May amid capital outflows. Indonesian authorities have drafted in more doctors and nurses to two areas on the islands of Java and Madura after hospitals there approached full capacity, raising worries of a potentially broader spike in cases that has hit other Asian countries in recent weeks. Singapore stocks trimmed earlier losses that were largely in real estate firms and banks. The city-state, a low-tax jurisdiction, will change its tax system as needed, its finance minister said after a group of seven advanced economies agreed to a mininum global corporate rate. Singapore is home to a number a global multinational firms" regional headquarters, including several tech giants. HIGHLIGHTS: ** Indonesian 3-year benchmark yields fell 5.4 basis points to 4.85%​​ ​​ ** SATS Ltd and Singapore Airlines Ltd gained the most; Comfortdelgro Corp Ltd fell 1.2% Asia stock indexes and currencies at 0634 GMT COUNTRY FX RIC FX FX INDEX STOCKS STOCKS DAILY % YTD % DAILY % YTD % Japan -0.19 -5.67 -0.19 5.54 China +0.09 +2.15 -0.67 2.95 India -0.05 +0.31 -0.14 12.50 Indonesia +0.00 -1.54 -0.81 0.69 Malaysia +0.15 -2.43 0.48 -2.53 Philippines -0.08 +0.67 0.68 -4.62 S.Korea -0.12 -2.51 -0.13 13.03 Singapore -0.02 -0.18 -0.10 11.57 Taiwan +0.06 +2.84 -0.05 15.91 Thailand -0.03 -3.94 -0.09 11.16 (Reporting by Nikhil Kurian Nainan in Bengaluru, Editing by Shri Navaratnam and Rashmi Aich) Our Standards: The Thomson Reuters Trust Principles.