* MSCI all-country index down 0.3 pct; Europe falls 1 pct
* Flattening US yield curve stokes recession concerns
* German 10-year yields at six-month low; curve also flattens
* Sterling volatile as Brexit debates continue
* Oil falls as trade woes stoke demand concerns
* (Updates throughout)
By Sujata Rao
LONDON, Dec 5 (Reuters) - World stocks tumbled to one-week lows on Wednesday, as declines by long-dated U.S. bond yields and a renewal of trade concerns stoked fears of a downturn in the world's biggest economy, the United States.
U.S. markets are shut to mark former President George H.W. Bush's death, but the effect of Wall Street's turmoil in the previous session, when New York-listed shares tumbled more than 3 percent, is being felt in Asia and Europe.
That pushed MSCI's all-country index down almost half a percent.
The declines came just a day after an equity surge driven by optimism that China and the United States would sort out their trade dispute. Then President Donald Trump threatened "major tariffs" on Chinese imports if his administration failed to reach an effective trade deal with Beijing.
"As I look into next year, most expectations for further gains have been pared back. Investors have gone from extended bullishness at the start of the year on equities to an uncomfortable neutrality," said Paul O'Connor, head of multi-asset at Janus Henderson.
Trump's comments, alongside the drop in U.S. stocks and bond yields, took Asian shares outside Japan 1.5 percent lower. Shanghai markets fell 0.6 percent, their losses limited by Chinese officials expressing confidence that a trade deal would be clinched on time.
European markets opened lower, with a pan-European index down 1.2 percent. Losses were led by a 1.6 percent decline in bank shares, which are being pummelled by the latest declines in long-dated government bond yields.
The moves follow similar declines in U.S. bank shares , which dropped 4.4 percent on Tuesday.
Global equities have been shaken by fears of a recession, fanned by the flattening U.S. Treasury yield curve -- a phenomenon in which longer-dated debt yields fall faster than their shorter-dated counterparts.
Such an inversion of two-year and 10-year yields, when 10-year bonds yield less than their two-year debt, has preceded every U.S. recession in the past 50 years.
"The market decline in the U.S. overnight and the flattening of the yield curve reflect that economic growth momentum is taking over as the primary concern for investors," Tai Hui, a strategist at J.P. Morgan Asset Management told clients.
So far, 10-year yields are clinging to an 11-basis-point margin over the two-year, although it was the smallest one in over a decade.
The flattening of the curve gained momentum after last week's signal by the Federal Reserve that it may be nearing an end to its three-year rate-increase cycle. It has spread to the euro zone, where the German 2-10 yield curve is at its flattest since mid-2017 at 85.70 basis points.
German 10-year yields slipped to six-month lows of 0.247 percent
"There has been a huge flight to safety in the European bond market ... (European) equities closed on Tuesday only modestly lower while there were sharp falls in the U.S.," Martin van Vliet, senior rates strategist at ING, said. "The European bond market was already preparing for trouble ahead."
Markets are also bracing for more news on the Brexit front. British Prime Minister Theresa May suffered embarrassing defeats one Tuesday, the start of five days of parliamentary debate over her plans to leave the European Union.
The pound touched 17-month lows of $1.2659 on Tuesday, then recovered to trade around $1.2734 on Wednesday, flat for the day.
The dollar has been undermined by the bond market moves and recession fears, but it has recovered from two-week lows against a basket of currencies to trade around 97, also flat on the day.
It rose 0.2 percent to 113 yen after losing 0.75 percent the previous day against the safe-haven Japanese currency.
The threat of slowing economic activity also weighed on oil prices. Brent futures shed more than one percent to $61.4 per barrel.
Reporting by Sujata Rao; additional reporting by Shinichi Saoshiro in Tokyo, Virginia Furness in London; editing by Larry King