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

* Nikkei bounces 1.8%, still down for week

* China PMI at 50 as expected, services stronger

* WHO confident China steps will contain virus

* Amazon surges 11% as sales beat expectations

By Wayne Cole

SYDNEY, Jan 31 (Reuters) - Asian share markets were fighting to stabilise at the end of a punishing week as investors clutched at hopes China could contain the coronavirus, even as headlines spoke of more cases and more deaths.

Supporting sentiment were surveys showing Chinese manufacturing activity held steady in January while services actually firmed, though this was likely before the virus took full hold.

Indeed, reports some Chinese provinces were asking companies not to re-start until Feb. 10 suggested activity would take a hard knock this month.

For now, sentiment got a timely boost when Amazon's sales blew past forecasts and sent its stock soaring 11% after hours, adding over $100 billion in market worth.

MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.4%, but was still down 3.8% on the week so far. Its 2.3% dive on Thursday had been the sharpest one-day loss in six months.

Japan's Nikkei bounced 1.8%, recouping half of its weekly loss. E-Mini futures for the S&P 500 firmed 0.2%, having rebounded late Thursday to end up 0.5%.

The World Health Organization on Thursday declared a global emergency as the virus spread to more countries.

Tedros Adhanom Ghebreyesus, WHO director-general, said the greatest worry was the potential for the virus to spread to countries with weaker health systems.

Yet investors took heart from comments that the drastic steps Beijing was taking would "reverse the tide" and contain the outbreak.

"Some shorts covered after the director gave the WHO's stamp of approval to China's aggressive containment effort," said Stephen Innes, Asia Pacific market strategist at AxiCorp.

"For now, the market's risk lights have shifted from flickering on red to a steady shade of amber, which could bring more risk back into play."

Wall Street quickly recouped its losses and ended higher in the wake of the WHO comments.

The Dow finished up 0.43%, while the S&P 500 gained 0.31% and the Nasdaq 0.26%. After the bell, NASDAQ futures pushed 1.3% higher on the Amazon results.

Still, the flow of news on the virus remained bleak with China's Hubei province reporting deaths from the disease had risen by 42 to 204 as of the end of Jan. 30.

More airlines curtailed flights into and out of China and companies temporarily closed operations, while Italy became the latest country to confirm cases of the virus.