* Asian stock markets : tmsnrt.rs/2zpUAr4 * Japan, China shares gain * U.S., Europe set to open higher ahead of U.S presidential debate Sept 29 (Reuters) - Asian markets hunkered down on Tuesday ahead of the first U.S. presidential debate later in the global day, with investors also remaining cautious over the global economy’s prospects as coronavirus deaths surpassed the 1-million mark worldwide. U.S shares were set to open higher with E-mini futures for the S&P 500 up 0.43%, while London’s FTSE futures were up 0.22% and eurostoxx 50 futures were up 0.34%. “Globally, a loss of momentum and the renewed rise in COVID-19 infection rates points to the need for additional fiscal and monetary support. That policy outlook is continuing to provide a supportive backdrop to equities despite recent volatility,” ANZ Bank analysts wrote in a note. Japan’s benchmark Nikkei average edged up 0.22% into positive territory while China’s blue-chip CSI 300 index climed 0.51%. MSCI’s broadest index of Asia-Pacific shares outside Japan rose 0.31% to 554.56. Hong Kong’s Hang Seng index however was down 0.24%, wiping out morning gains. Australia’s S&P/ASX 200 index also fell back to trade flat after earlier touching its highest level in three weeks. New Zealand’s S&P/NZX 50 index lost 0.51%. Asian markets have been buoyed by positive signs around China’s economic recovery, although the coronavirus pandemic continues to wreak economic havoc globally and raise concern about high valuations. But trade in Asia was subdued ahead of China’s Golden Week holiday, from Oct.1-8, and other national holidays in the region. The first U.S. presidential debate is scheduled later in the global day (Wednesday 0100 GMT), otherwise investors’ focus was locked on U.S. lawmakers efforts to cobble together additional economic stimulus. U.S. House of Representatives Speaker Nancy Pelosi was set to hold further talks with Treasury Secretary Steven Mnuchin on Tuesday morning in Washington. U.S. consumer confidence and home price data is also due later. Upcoming U.S. economic data should help show how well the country is positioned to rebound from pandemic lockdowns, and how necessary more stimulus will be. Wall Street showed strong gains on Monday, particularly in hard-hit sectors like hotels, banks and airlines. But there was also cause for caution, as Europe is experiencing a rise in new COVID-19 infections and some U.S. states continue to grapple with high case numbers. Safe-haven spot gold was flat at around $1881 a an ounce. U.S. gold futures gained 0.21% to $1,876.7 an ounce. U.S. Brent crude slipped 16 cents to $42.27 a barrel while U.S. light crude was down 21 cents at $40.39 on demand worries. The U.S. dollar dropped from a two-month high against a basket of currencies Monday, with the dollar index falling 0.3%, its biggest daily percentage drop in roughly three weeks. Bonds were broadly steady. The yield on benchmark 10-year U.S. government debt fell further to 0.625%.