With U.S. markets closed for the Martin Luther King Day holiday, U.S. stock index futures slipped 0.3 percent <SPc1>.
European shares opened higher but any prospect of a rally after stocks hit their lowest since December 2014 on Friday quickly fizzled out.
The pan-European FTSEurofirst 300 index <.FTEU3>, which has lost more than 10 percent this year, dropped a further 0.2 percent, with an index of euro zone banks <.SX7E> down 3.3 percent.
An ECB spokesman said on Sunday a number of banks would be asked about high levels of non-performing loans. The burden of such loans, particularly in Greece, Portugal, Spain and Italy, is curbing the euro zone's economic recovery by limiting banks' ability to lend.
Portuguese stocks <.PSI20> were down 3.4 percent and Italy <.FTMIB> lost 2.3 percent
"The uncertainty in the market, be it in Europe or wherever else, is causing these banks to suffer," Mark Foulds, sales trader at ETX Capital, said, adding that the sector was also under pressure from recent volatility linked to China.
"When the markets fall like they have done, everyone feels on edge. The market is dire, and there's not the liquidity that there used to be, which can mean the market gets oversold."
Britain's FTSE 100 <.FTSE> index fell 0.4 percent.
Earlier, MSCI's broadest index of Asia-Pacific shares outside Japan <.MIAPJ0000PUS> fell to its lowest since October 2011, down 0.7 percent.
Japan's Nikkei <.N225> tumbled as much as 2.8 percent to a one-year low before closing down 1.1 percent. It has lost 20 percent from a peak hit in June, meeting a common definition of a bear market.
The volatile Shanghai Composite index <.SSEC> touched intraday lows last seen in August but closed up 0.4 percent. It remains down nearly 18 percent this month.
In oil markets, the prospect of a jump in Iranian crude exports after international sanctions against the country over its nuclear program were lifted at the weekend weighed heavily on oil.
Brent crude, the global benchmark, was last down 18 cents a barrel at $28.76 <LCOc1>, having earlier dipped below $28 for the first time since December 2003.
"The lifting of key sanctions should allow it (Iran) to increase crude exports this year by at least 500,000 barrels a day on average, putting further downward pressure on oil prices in the near term," Barclays analysts said in a note on Monday.
Analysts at JPMorgan said oil-producing countries will need to sell large quantities of stocks and bonds this year to cover shortfalls in their budgets resulting from the oil price slump.
They estimate sales of $110 billion bonds this year, up from $45 billion last year, and $75 billion of equities compared with $10 billion.
In currency markets the Chinese yuan rose 0.5 percent <CNH=> in offshore trade to 6.5830 per dollar, as Chinese authorities continued to stamp down on speculative yuan selling.
China will start implementing a reserve requirement ratio on some banks involved in the offshore yuan market, the People's Bank of China said on Monday, in what appears to be its latest attempt to stem speculation in the currency.
The safe-haven yen gave up some of its gains after having risen to a five-month high of 116.51 to the dollar <JPY=> on Friday. It stood at 117.34, down 0.3 percent on the day. The euro weakened 0.2 percent to $1.0890 <EUR=>.
The dollar has struggled to gain ground since the Federal Reserve's historic interest rate rise a month ago. After data on Friday indicating U.S. economic growth braked sharply in the fourth quarter, short-term interest rate futures <0#FF:> price in only one hike by year-end, compared with two priced in as the year began.
In European bond trading, yields were mostly flat.
(Additional reporting by Alistair Smout and Nigel Stephenson; Editing by Catherine Evans and John Stonestreet)
By Jamie McGeever