* Asian stock markets : tmsnrt.rs/2zpUAr4 * MSCI ex-Japan rises, edging closer to recent all-time high * Hopes of $1.9 trln U.S. stimulus, vaccines boosting sentiment * Strong company earnings season also aiding equities sentiment * U.S dollar retreats from recent highs * Oil near $60 a barrel SYDNEY, Feb 8 (Reuters) - Asian shares hovered near record highs on Monday while oil edged closer to $60 a barrel on hopes a $1.9 trillion COVID-19 aid package will be passed by U.S. lawmakers as soon as this month just as coronavirus vaccines are being rolled out globally. MSCI’s broadest index of Asia-Pacific shares outside Japan was last up 0.2% at 717.2, not far from last week’s record high of 730.6. Japan’s Nikkei climbed 0.3% while Australian shares advanced 0.5% led by technology and mining shares. E-mini futures for the S&P 500 rose 0.3% in early Asian trading. Hopes of a quicker economic revival and supply curbs by producer group OPEC and its allies pushed oil to its highest level in a year as it edged near $60 a barrel. Global equity markets have scaled record highs in recent days on hopes of faster economic revival led by successful vaccine rollouts and expectations of a large U.S. pandemic relief package. On Friday, the Nasdaq and S&P 500 hit all-time highs on stronger-than-expected corporate results in the fourth quarter and as companies were on track to post earnings growth for the first quarter instead of a decline. The rallies came even as U.S. data painted a dour picture of the country’s labour market with payrolls rising by 49,000, half of what economists were expecting. The weak report spurred the push for more stimulus, underscoring the need for lawmakers to act on President Joe Biden’s $1.9 trillion COVID-19 relief package. Biden and his Democratic allies in Congress forged ahead with their stimulus plan on Friday as lawmakers approved a budget outline that will allow them to muscle through in the coming weeks without Republican support. U.S. Treasury Secretary Janet Yallen predicted the United States would hit full employment next year if Congress can pass its support package. “That’s a big call given full employment is 4.1%, but one that will sit well with the market at a time when the vaccination program is being rolled out efficiently in a number of countries,” said Chris Weston, Melbourne-based chief strategist at Pepperstone. In currencies, the U.S. dollar came off a four-month high against the Japanese yen to be last at 105.39 following the weak jobs report. The euro edged up slightly after rising 0.7% on Friday to a one-week high of $1.2054. It was last at $1.2044. The risk-sensitive Australian dollar held near a one-week high at $0.7678. In commodities, Brent crude and U.S. crude climbed 52 cents each to $59.86 and $0.57.37 respectively. U.S. gold futures were up 0.2% at $1,817 an ounce.