* Graphic: World FX rates tmsnrt.rs/2egbfVh * Travel stocks fall in Malaysia * Banks power Singapore's index to a six-week high * Asian currencies slightly weaker By Anushka Trivedi Jan 7 (Reuters) - Malaysia shares sat out a broader rally in Asian stocks on Thursday as climbing COVID-19 cases at home spooked investors, while Singapore and South Korea indexes led gains on hopes that a large U.S. stimulus would boost trade and investment. India's benchmark index touched an all-time high, while equities in South Korea surged 2% to break above the 3,000 handle again. Indonesia, Thailand and Taiwan equities all rose more than 1%. Singapore's Straits Times Index, that had lagged its peers in the year-end rally in 2020, hit a six-week high, propelled by heavyweight banking stocks that tracked their U.S. counterparts. Democrat victories in two Georgia races handed them control of the Senate in the United States, making it easier for incoming President Joe Biden to push his reforms which includes higher fiscal spending, with markets expecting it to drive economic growth. "More fiscal stimulus would lead to a weaker U.S. dollar and that is always positive for emerging and Asian markets," said Joel Ng, an analyst at KGI Securities in Singapore. It would also increase demand for commodities which should benefit emerging markets that are large exporters, he added. Meanwhile, the Kuala Lumpur index fell as much as 1.2% after adding 2,593 coronavirus cases to its tally by Wednesday, the director general of health said here, further straining the country's healthcare system. Travel stocks led declines on the benchmark, while heavyweight latex glove makers surged. Several local media outlets here reported here the Malaysian government was mulling targeted lockdowns after New Year celebrations increased caseload, including in Sabah, one of the worst hit by the pandemic. Most Asian currencies were marginally weaker against a flat greenback, with the Singapore dollar, Malaysian ringgit and the Indonesian rupiah easing 0.1% each. Taiwan's dollar was an outlier, firming 1.5% to hover at an about 23-year high, a day after the region's central bank admitted it had intervened in the forex market owing to a flood of foreign capital. Taiwan's foreign exchange reserves rose by a record $16.514 billion in December, unnerving its government, as it is wary of being labelled a currency manipulator by Washington, the island's most important international backer. HIGHLIGHTS ** Indonesian 10-year benchmark yields are down 0.2 basis points at 6.01% ** Top gainers on the Singapore STI include DBS Group Holdings Ltd up 3.4%, and Yangzijiang Shipbuilding Holdings Ltd up 3.1% ** Top losers on FTSE Bursa Malaysia Kl Index include Genting Malaysia Bhd and Genting Bhd down about 3% each Asia stock indexes and currencies at 0714 GMT COUNTRY FX RIC FX DAILY % FX YTD % INDEX STOCKS DAILY STOCKS YTD % % Japan -0.23 -0.04 1.60 0.17 China +0.12 +1.12 0.67 2.92 India -0.03 -0.08 0.29 1.47 Indonesia -0.14 +1.01 1.31 2.78 Malaysia -0.12 +0.17 -0.20 -2.36 Philippines -0.04 -0.08 1.02 -0.28 S.Korea -0.16 -0.10 2.14 5.51 Singapore -0.07 +0.18 1.50 2.19 Taiwan +1.55 +1.82 1.54 3.27 Thailand -0.20 +0.10 1.48 4.49 (Reporting by Anushka Trivedi and A K Pranav in Bengaluru, additional reporting by Rozanna Latiff in Kuala Lumpur; Editing by Shailesh Kuber)