Australian S&P/ASX 200 futures lost 0.76% in early trading, Japan's Nikkei 225 futures added 0.22%, and Hong Kong's Hang Seng index futures rose 0.39%.
Asian shares are showing a mixed picture on Tuesday after a volatile day in U.S. equity markets amid persistent concerns over the record number of new coronavirus cases worldwide and signs of an economic rebound.
Australian S&P/ASX 200 futures lost 0.76% in early trading, Japan's Nikkei 225 futures added 0.22%, and Hong Kong's Hang Seng index futures rose 0.39%.
E-mini futures for the S&P 500 rose 0.21%.
After a strong start in the United States, equity markets sold off when California announced it was slowing the state‘s reopening, shutting bars and banning indoor restaurant dining statewide in response to a surge in coronavirus cases.
But at the same time, U.S. consumers reported being more optimistic that the worst of their economic woes from the pandemic were behind them, complicating the picture for investors about the state of the world's largest economy.
"The U.S. continues to report fresh highs of daily new infections. However, the seriousness of the disease is falling. Hospitalisation rates...has trended down since April," said Kim Mundy with the Commonwealth Bank of Australia in Sydney, in an analyst note. "The upshot is the surge in infections does not give the full story. And it suggests the U.S. is learning to live with the disease."
Tensions also grew between the U.S. and China over disputed claims to offshore resources throughout the South China Sea, with U.S. officials saying China's claims were "unlawful."
The U.S. dollar edged lower on Monday as investors looked to U.S. corporate earnings and upcoming retail data to gauge whether guarded optimism on the economic outlook was justified. Spot gold dropped 0.1% to $1,801.30 an ounce.
On Monday, the S&P 500 dropped 0.94% after touching its highest level since Feb. 24 earlier in the trading day. The tech-heavy Nasdaq Composite dropped 2.13%, driven by declines in some outperforming big names, including Amazon and Microsoft . The Dow Jones Industrial Average rose 0.04%.
MSCI's gauge of stocks across the globe briefly touched its highest level since February, before ending down 0.29%.
Growing concerns over the coronavirus spread and simmering U.S.-China tensions also weighed on oil. Brent futures fell 52 cents, or 1.2%, to settle at $42.72 a barrel.
In upcoming data, China is set to report Tuesday its trade numbers, with slump in China's exports likely easing in June while imports contracted less sharply on higher crude oil and commodities purchases, according to a Monday Reuters poll.