* Asian stock markets: https://tmsnrt.rs/2zpUAr4

* Financial markets trying to shake off virus woes

* Equities draw investors on hopes for more China stimulus

* Oil markets worried about demand disruptions

By Stanley White

TOKYO, Feb 5 (Reuters) - Asian stocks steadied on Wednesday on hopes of additional Chinese stimulus to lessen the economic impact of a coronavirus outbreak, but risks remain as the illness continues to spread and the death toll neared 500.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 0.3%. Australian shares were up 0.58%, while Japan's Nikkei stock index rose 1.19%.

The safe-haven yen and Swiss franc nursed losses versus the dollar while the yuan held on to gains in offshore trade in a tentative sign of improvement in risk appetite as investors monitor the impact of the virus.

Oil prices, however, remained weak on worries about a long-term dent in demand for energy and other commodities despite hopes for more output cuts from OPEC and its allies.

China and other countries have imposed travel restrictions to try to contain a new virus that emerged in the central Chinese city of Wuhan late last year, slamming the breaks on manufacturing and tourism in the world's second-largest economy.

Many investors argue that any slowdown will be temporary and that Chinese policy steps are reason to remain optimistic about the growth outlook, but so far public health officials have not found a way to stop the spread of the virus both inside and outside of China.

"We're going to have a strong day in Asia, but whether this is the reversal of a downtrend remains to be seen," said Michael McCarthy, chief market strategist at CMC Markets in Sydney.

"Oil investors remain pessimistic about demand disruptions, but equity investors, especially overseas, are discounting the impact of the virus."

U.S. stock futures fell 0.18% in Asia on Wednesday. The S&P 500 rose 1.5% on Tuesday and the tech-heavy Nasdaq rose to a record high.

The People's Bank of China (PBOC) is likely to lower its key lending rate - the loan prime rate - on Feb. 20, and cut banks' reserve requirement ratios in the coming weeks, policy sources told Reuters.

The PBOC has already pumped hundreds of billions of dollars into the financial system this week. This helped Chinese stocks stabilise on Tuesday following a rout that wiped out around $700 billion in market capitalisation on Monday when Chinese markets opened after an extended holiday.

The virus has already claimed nearly 500 lives. Japan's health minister said on Wednesday 10 people on a cruise ship at the port of Yokohama have tested positive for the new virus.