Bargain-buyers tried to step in after the latest sell-off but were unable to gain traction, with fears about the outlook for the global economy keeping sentiment beaten down.
The China-US trade row, signs of softness in both countries' economies, the Huawei arrest, Brexit, demonstrations in France and tanking oil prices are among the problems facing investors, and analysts warned of more volatility to come.
Adding to those problems is upheaval in India -- another crucial economy -- where the head of the central bank has resigned following a row with Prime Minister Narendra Modi's administration over alleged government interference.
Monday's development hammered the rupee, which was already Asia's worst-performing currency, and battered the Sensex stock market. Futures point to another sell-off when they reopen later in the day.
Global risk sentiment "is facing a towering wall of worry as virtually every major economy in the world is slowing, suggesting the synchronised global slowdown is accelerating at a much faster pace than thought," said Stephen Innes, head of Asia-Pacific trade at OANDA.
In early Asian trade Hong Kong was down 0.1 percent and Tokyo ended the morning 0.6 percent lower, with Singapore 0.2 percent off.
However, Shanghai, Sydney and Wellington each edged 0.2 percent higher, while Seoul gained 0.1 percent and Manila put on one percent.
On currency markets the pound was stuck around levels last seen in April 2017, having dived 1.6 percent Monday in reaction to Prime Minister Theresa May's decision to delay Tuesday's parliamentary vote on her Brexit deal.
May recognised the agreement would be voted down and promised to get clarity from Brussels on the key issue of Northern Ireland, but the decision ramped up uncertainty and fuelled fresh questions about her political future.
Adding to the problems, the PM did not provide a timetable for a new vote.
"The market is concerned that the postponement uses up valuable time before the 29th March exit date, and the risk of a no-deal scenario is growing" said National Australia Bank economist David de Garis.
On an upbeat note, Beijing's economics point man Vice Premier Liu He spoke with US officials to flesh out a timetable for talks to resolve their trade row, following this month's G20 truce hammered out between Donald Trump and Xi Jinping.
"It's a positive signal that work is in progress," said Michelle Lam, a greater China economist at Societe Generale.
However, there are low expectations the two sides can reach a full-blown agreement that will end their trade war, with the waters muddied by the arrest of a top executive at Chinese telecoms giant Huawei.
Meng Wanzhou, Huawei's chief financial officer and daughter of the firm's founder, faces US fraud charges related to allegedly breaking Iran sanctions but has asked for bail.
The arrest has angered China and led to concerns it could derail the trade talks.
Both main oil contracts inched higher but were well short of making up for the three percent losses suffered Monday on concerns an output cut agreed by OPEC at the weekend might not be enough to lift process and offset a supply glut.
Key figures around 0230 GMT
Tokyo - Nikkei 225: DOWN 0.6 percent at 21,100.30 (break)
Hong Kong - Hang Seng: DOWN 0.1 percent at 25,716.45
Shanghai - Composite: UP 0.2 percent at 2,590.41
Pound/dollar: UP at $1.2568 from $1.2562 at 2200 GMT
Euro/dollar: UP at $1.1360 from $1.1354
Dollar/yen: DOWN at 113.10 yen from 113.35 yen
Oil - West Texas Intermediate UP 18 cents at $51.18 per barrel
Oil - Brent Crude: UP 24 cents at $60.21 per barrel
New York - Dow Jones: UP 0.1 percent at 24,423.26 (close)
London - FTSE 100: DOWN 0.8 percent at 6,721.54 (close)
Published : December 11, 2018
By : Agence France-Presse Hong Kong