HONG KONG, Oct 7 (Reuters) - Asian shares rallied on Thursday, supported by a possible easing in U.S.-China tensions, and weaker energy prices, as oil edged down from multi-year highs. U.S. and European futures also bounced with S&P 500 futures rising 0.52%, and pan-region Euro Stoxx 50 futures gaining 1.23% in early trade a day after the Euro STOXX 600 (.STOXX) index dropped 1.03% MSCI"s broadest index of Asia-Pacific shares outside Japan (.MIAPJ0000PUS) rose 1.45%, which if it holds, would be the benchmark"s best daily performance since August. Hong Kong (.HSI)led Asia"s gains. The index rose 2.41%, bouncing from its lowest close in 12 months, and was headed towards its best day since August, though analysts remained cautious. "It"s too early to say this is part of a turnaround. Today there seems to be some bottom fishing and short covering going on, and also a possible meeting between President Xi Jinping and President Joe Biden is helping the mood," said Steven Leung executive director for institutional sales at UOB Kay Hian in Hong Kong. The United States and China have agreed in principle for their presidents to hold a virtual meeting before the end of the year, a senior U.S. administration official said on Wednesday. read more Elsewhere, South Korea"s Kospi (.KS11) gained 1.6%, Australian shares (.AXJO) rose 0.51%, and Japan"s Nikkei (.N225) firmed 0.72%, snapping eight days of losses. However, there were still reasons for caution around the region, especially with China on holiday, seemingly contributing to a delay in progress towards any resolution for beleaguered developer China Evergrande (3333.HK). Carlos Casanova, senior Asia economist at UBP, said there were ongoing concerns about China"s power crunch and its property market, given the government did not seem to in a hurry to step in even as debt problems at Evergrande threatened to spill over into the wider industry. read more "There is contagion into the broader real estate sector, authorities are not doing more to intervene, and so investors are trying to assess what this new pain threshold means," he said. But he added that the improved mood in U.S.-China relations, especially the more constructive tone in the speech by trade chief Katherine Tai this week, had boosted risk sentiment. Also supporting equities, oil prices pulled away from multi-year highs hit a day earlier. An rally in oil prices had been a major contributor to a sell-off in equities this week. U.S. crude dipped 0.93% to $76.71 a barrel. Crude fell overnight after hitting a seven-year high of $79.78 on Wednesday on an unexpected rise in U.S. crude stocks. Brent crude lost 0.5% to $80.69 per barrel, off its three-year high of $83.47 also hit on Wednesday. European and U.S. natural gas prices also both slipped over 10% overnight in volatile trade. European prices had hit all-time highs early on Wednesday amid an enduring supply crunch. The recent surge in global gas prices – that have helped lift Asian LNG prices by 500% from a year ago – have left the entire energy area prone to increased volatility, with power producers in Europe and Asia still expected to replenish tight stocks ahead of winter. read more The fall in energy prices and apparent temporary deal to avert a federal debt default contributed to a late rally on Wall Street. read more Global markets will next focus on payrolls data due on Friday, with investors anticipating that a reasonable figure will mean the U.S. Federal Reserve will begin tapering its massive stimulus programme at its November meeting. The dollar was steady, not too far from 12-month highs hit last month against a basket of currencies , and held at a 14-month high against the euro. The yield on benchmark 10-year Treasury notes was at 1.5398%, off Wednesday"s three and a half month high of 1.573%.