Asian shares outside Japan edged up 0.2%, while E-Mini futures for the US S&P 500 added 1.1%, even as China said it opposed the latest US rules against Huawei.
"Between fears of sustained economic damage from the global health crisis and hopes for recovery as economies gradually reopen, we are seeing the latter reigning into the start of the fresh week for US futures," said IG market strategist Jingyi Pan.
Singapore's benchmark index rose 0.8%, as annual exports rose for the third straight month in April, bolstered by a sharp rise in pharmaceutical shipments, according to official data.
Serving as the bellwether for Asia's trade picture, non-oil domestic exports rose 9.7% in April, against a 5% decline forecast in a Reuters poll.
Real estate stocks Capital and Mall Trust and Mapletree Commercial Trust were the top gainers on the benchmark, climbing 4% and 3.3%, respectively.
Thailand's index advanced, after a tepid session on Friday where the index closed flat, buoyed by a jump in oil prices.
Thailand's economy contracted at its sharpest pace in eight years in the first quarter but by less than expected. Southeast Asia's second-largest economy shrank 1.8% in the first quarter from a year earlier, while a Reuters poll expected a 4.0% contraction.
Energy stocks boosted the index, with Lanna Resources jumping as much as 14.4%, while Prima Marine added 3.8%. Bucking the regional trend, Philippine shares dropped 1.2% to their lowest in nearly three weeks, with industrials and telecommunications services weighing the most.
Earlier in the session, shares of the Philippines' biggest broadcaster ABS-CBN Corp slumped as much as 14.3% after the telecoms regulator ordered it to shut down operations.