Oil prices extended recent sharp losses, trading below $85 a barrel on expectations that slowing global economic growth will crimp demand for crude.
Japan's Nikkei 225 stock average was down 1.3 percent at 9,178.30 and Seoul's Kospi dropped 1.6 percent to 1,913.58.
Hong Kong's Hang Seng tumbled 2.6 percent to 20,409.01 while Australia's S&P/ASX 200 pared its initial sell-off to be down 1 percent at 4,062.70.
Futures pointed to losses on Wall Street when it opens Monday. Dow futures were off 225 points, or 2 percent, at 11,177 and broader S&P 500 futures shed 23.6, or 2 percent, to 1,174.20.
Standard & Poor's downgrade of the U.S. sovereign credit rating to AA+ from the top-notch AAA - announced late Friday - is another blow to confidence in the struggling U.S. economy, analysts said.
Worries that the U.S. economy, the world's biggest, is heading back into recession have been compounded by signs that Europe's government debt crisis is threatening to engulf bigger economies such as Italy and Spain.
"The loss of AAA status will plainly add some salt to the wounds of weak sentiment" in stock markets but concern is likely to quickly return to the prospects for U.S. and global economic growth, DBS Bank Ltd. in Singapore said in a report.
"Investors are far more concerned about the weak economy than what the S&P has to say about US politicians and their inability to wrap a plan around the deficit," the DBS analysts said.
A flurry of weekend activity by global finance officials gave rise to hopes of coordinated action to prevent a market meltdown.
The G-7 industrial countries issued a joint statement late Sunday pledging increased cooperation to attack economic problems and saying they were committed to taking all necessary measures to support financial stability and growth.
The G-7 statement came after the group held an emergency conference call to discuss the debt crisis in Europe and market prospects following the announcement of the first-ever downgrade of the credit rating of the U.S. government.
The European Central Bank, meanwhile, said it will "actively implement" a bond-purchase program that could boost Spanish and Italian bonds and drive down interest yields that threaten those countries with financial disaster.
The burst of activity underscored how government debt levels in Europe and the U.S. have unsettled financial markets - and sharpened fears that debt troubles could derail the global recovery from the 2007-2009 financial crisis.
Elsewhere in Asia, Taiwan's benchmark index slipped 1.6 percent and New Zealand's market dropped 2.2 percent. Singapore's key index retreated 1.8 percent.
The Dow fell 5.8 percent last week amid dour U.S. economic news. It plunged 513 points on Thursday alone, the worst day for the Dow since the global financial crisis erupted in 2008.
Benchmark oil for September delivery was down $2.55 to $84.33 a barrel in electronic trading on the New York Mercantile Exchange.
