* Graphic: World FX rates in 2020 http://tmsnrt.rs/2egbfVh
* S&P E-mini futures up 0.3%
* MSCI All Country World down 0.34%
* European shares slump after attempted recovery
* Short-lived relief in stocks
By Ritvik Carvalho
LONDON, Feb 25 (Reuters) - Global stocks sank to their lowest levels in over two months on Tuesday, as relief from a sharp selloff the previous day on fears about the spreading coronavirus proved temporary.
European shares recorded their worst one-day loss since June 2016 on Monday as worries about the spread of the new virus far beyond China whacked global markets and risk sentiment.
On Tuesday, the pan-European STOXX 600 index initially rose 0.6% in London but was down 0.3% by early afternoon. Italian shares lost 0.3%, adding to their earlier losses. Italy is grappling with the worst outbreak of coronavirus in Europe.
More than 80,000 people have been infected in China since the outbreak began, apparently in an illegal wildlife market in the central city of Wuhan late last year.
China's death toll was 2,663 by the end of Monday, up 71 from the previous day. But the World Health Organization (WHO) has said the epidemic in China peaked between Jan. 23 and Feb. 2 and has been declining since.
"In spite of increased uncertainty in Europe, signs remain good that China is succeeding in containing the outbreak there," said Mark Haefele, chief investment officer at UBS Global Wealth Management.
"The number of new cases in China ex-Hubei are now at very low levels, which should allow economic activity to normalize and supply chain disruption to begin to resolve itself, in line with our base case."
MSCI's All Country World index, which tracks shares across 47 countries, was down 0.33% by 1237 GMT. The index suffered its biggest daily drop in two years on Monday.
Southern Europe's bond markets, which earlier showed signs of stabilising, gave way to fresh selling of not just Italian bonds, but also Greek, Spanish and Portuguese debt.
E-Mini futures for the S&P 500, which earlier bounced 0.7%, pared some of those gains to trade only 0.3% higher.
In Asia earlier, South Korea's hard-hit market eked out a 0.6% rise and helped MSCI's broadest index of Asia-Pacific shares outside Japan fight back to flat.
Japan's Nikkei was down 3.4%, catching up with the global sell-off after having been shut on Monday, while Shanghai blue chips eased 1.6%.
European and U.S. stocks have suffered their biggest loses since mid-2016 amid fears the coronavirus may be morphing into a pandemic that could cripple global supply chains and wreak far greater economic damage than first thought.
The risks are such that bond markets are starting to bet central banks will have to ride to the rescue with new stimulus.
Futures for the Federal Reserve funds rate have surged in the last few days to price in a 50-50 chance of a quarter-point rate cut as early as April. In all, they imply more than 50 basis points of reductions by year end.
Central banks across Asia have already been easing policy, while governments have promised large injections of fiscal stimulus, something western countries might also have to consider.
Data showing sales of smartphones in China tumbled by more than a third in January, underlining the potential economic impact of the virus, helped knock Apple Inc shares 3.5% lower on Monday.
BONDS BET ON RATE CUTS
The coronavirus death toll climbed to seven in Italy on Monday and several Middle East countries were dealing with their first infections, feeding worries about a pandemic.
The rush to bonds left yields on 10-year U.S. Treasury notes at 1.39%, down almost 20 basis points in just three sessions and paying less than overnight rates. Yields are rapidly approaching the all-time low of 1.321% hit in July 2016.
The sharp drop, combined with the fact the Fed has far more room to cut interest rates than its peers, kept the U.S. dollar restrained after a run of strong gains.
"Besides a tapering in the geographical spread of the coronavirus or unexpected improvements in key short-term macro indicators, the circuit breaker for these market moves is starting to move towards the U.S. central bank," Danske Bank said in a note to clients.
In currencies, the fell 0.2% to reach $1.0835, while the dollar lost 0.1% to trade at 110.61 yen, away from a 10-month top of 112.21.
Against a basket of currencies, the greenback traded flat .
Gold ran into profit-taking after hitting a seven-year peak overnight, and was last down 0.7% at $1,649.26 an ounce.
Oil steadied after shedding nearly 4% on Monday. U.S. crude was down 0.43% at $51.23, while Brent crude also lost 0.43% to $56.06.
(Reporting by Ritvik Carvalho; Additional reporting by Wayne Cole in Sydney; Editing by Catherine Evans)