The death toll from the virus crossed the 200-mark in China with confirmed cases of infection reported in at least 22 other countries and regions.
The WHO director-general on Thursday said the greatest concern was the virus' potential spread to countries with weaker healthcare systems, compounded by cases of person-to-person transfer of the virus outside China.
Economists have signalled the impact of the new virus could be worse than that of the Severe Respiratory Syndrome (SARS) epidemic in 2002-2003, which took 800 lives and cost the global economy an estimated $33 billion.
All south-east Asian markets were headed for weekly losses as the virus continued to dampen risk appetite in the region.
Providing some relief, China's manufacturing activity in January was in line with expectations, dodging a contraction.
"China markets' return in the coming week will be assessed for impact and could add to the noise as selling gets underway," IG Market Strategist Jingyi Pan said in note.
With the growing reassessment of the growth trajectory for China this year by brokers following the virus outbreak, the sentiment may be overtly bearish at present, the note added.
Indonesian shares slumped as much as 1.7% and were on course to slip 4.2% for the week, with financial and consumer stocks being the biggest drags on the index.
An index of Indonesia's 45 most liquid stocks <.JKLQ45> fell over 2%.
Bank Rakyat Indonesia shed 2.6% and household goods maker Unilever Indonesia dipped 2.7%.
Philippine stocks lost 1.8%, on course for a fifth consecutive session of losses and were set to be down 4.8% for the week.
Financials and consumer stocks took the biggest hit, with BDO Unibank and conglomerate SM Investments dropping 2.9% and 2.2%, respectively.
Singapore shares dipped 0.3% and headed for a loss of about 1.8% for the month, with conglomerate DBS Group Holdings losing 1.4% and Mapletree Logistics Trust down 1.1%.
Vietnamese stocks fell nearly 1% after losing over 3% in the previous session.
The Malaysian index inched lower 0.1%, following eight consecutive sessions of losses.
The Thai bourse inched 0.3% lower, ahead of trade data for December expected later on Thursday.
By Arpit Nayak