* Coronavirus cases rise, Asian markets slip
* Nikkei, Kospi down but poised for best week in 2020
* Major currencies steady, oil rises but has not recovered
* Asian stock markets: tmsnrt.rs/2zpUAr4
By Tom Westbrook
SINGAPORE, Feb 7 (Reuters) - Asian share markets slipped on Friday and oil price gains stalled, as the growing death toll and economic damage from the coronavirus outbreak put a lid on the week's sharp rally.
The toll in mainland China from the new virus rose to 636, more than doubling in just under a week, with the number of infections at 31,161.
In the early hours of the morning one of the first Chinese doctors to raise the alarm about the virus died from the illness at a hospital in Wuhan, the outbreak's epicentre.
MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.7%. Japan's Nikkei and Korea's Kospi were in the red. Hong Kong's Hang Seng fell 0.6% and the Shanghai Composite was 0.1% weaker.
Barring Shanghai, which has recovered about half of its $400 billion wipeout on Monday, all are ahead for the week, amid a broad global rally.
That has been underpinned by China's sweeping efforts to contain the spread of the virus. But with deaths rising, cities shut off, flights cancelled and factories closed, global supply chains are in disarray and fears of a pandemic remain high.
"The rate of infection is not slowing," said Michael McCarthy, chief markets strategist at brokerage CMC Markets in Sydney.
"I'm a little surprised at the way European and U.S. investors have shrugged this off. I think the reaction in the Asia-Pacific region is much more reasonable. There is real uncertainty," he said.
U.S. stocks overnight gained for a fourth straight session and Wall Street's main indexes hit record highs, while Asian assets - particularly currencies - remain under pressure.
In Asian trade, the steepest weekly slide in the yen since October has paused, leaving the currency sitting just above a two-week low at 109.93 per dollar.
Gains in the Australian dollar, a liquid proxy for China because of the heavy exposure of Australian exports, were likewise halted.
While the Aussie is on track for its first weekly gain this year, elsewhere in Asia the Singapore dollar and Thai baht have been trampled in a rush from emerging market currencies into majors.
Chinese goods trade figures due Friday will be closely watched for an early glimpse of how the virus, and the harsh measures to contain it, are affecting the flow of goods.
Much is unknown about the coronavirus, including its lethality and transmission routes. The World Health Organization has said it is too early to call a peak in the outbreak.
Yet China's aggressive response, dubbed a "people's war for epidemic prevention" by President Xi Jinping, appears to have inspired confidence.
Beijing has pumped billions of dollars into the money market to stabilise market confidence and the central bank said on Friday it expects the virus impact to be temporary.
Yet, owing to much greater exposure to Chinese demand and less access to the benefits of monetary stimulus, commodity prices have been more sensitive to conditions on the ground.
Oil and metal prices fell hard as the coronavirus outbreak gained pace and have been slow to recover.
U.S. crude was firm on Friday at $51.31 per barrel, but is flat for the week and remains 13% below its Jan. 21 level. Brent prices were last at $55.33 per barrel.
A rally in copper - often seen as a barometer of global economic health because of its wide industrial use - ran out of steam on Thursday and closed flat in London at $5,735-a-tonne .
"We think that demand could come back strongly as opposed to gradually in Q2 2020," said Commonwealth Bank commodities analyst Vivek Dhar.
"But the risk in the near term is that provinces take longer to return to work in order to contain the spread of the virus." (Additional reporting by Melanie Burton in Melbourne; Editing by Shri Navaratnam and Lincoln Feast.)