* German Bund yield hits record lows
* Dutch 10-yields negative for first time since 2016
* Trump Mexico tariff news, China PMI raise recession fears (Updates throughout)
LONDON, May 31 (Reuters) - Germany's 10-year bond yield fell to record lows on Friday, after U.S. President Donald Trump's sudden threat to impose tariffs on Mexican goods sent shock waves through world markets and heightened fears of economic recession.
Seen as unthinkable even a few weeks ago, the relentless fall in yields in what is seen as one of the world's safest assets -- German government debt -- speaks to the scale of pessimism gripping investors.
"The Trump Mexico tariffs surprised me and more so than the escalation in the trade war with China," said Jan von Gerich, chief market strategist at Nordea. "This news is negative for markets and the economic outlook."
The global outlook darkened further and a rally in so-called safe assets -- government bonds, yen and gold -- accelerated after a key measure of Chinese manufacturing activity in May disappointed.
And dovish comments from the U.S. Federal Reserve's Richard Clarida, saying the Fed would act if inflation stays too low or global risks endanger the economic outlook, added to a sense that a U.S. rate cut could come sooner rather than later.
Germany's 10-year bond fell more than three basis points to minus 0.209%, an all-time low. It surpassed a previous record low hit in July 2016 just after Britain voted to leave the European Union.
The yield is down more than 20 basis points this month.
"Bund yields are at historic lows even as there are no real rate cuts priced in the euro area," said Rishi Mishra, interest rates strategist at Futures First Info Services.
"It's either the biggest mispricing of the century, or Bund yields are headed below minus 50 bps."
Yields on Dutch 10-year bonds became the latest to drop into negative territory - moving below 0% for the first time since 2016, while French long-dated bond yields fell to their lowest since 2016 at just 0.22% and Spanish and Portuguese yields kept record lows in sight .
Greece's 10-year bond yield fell below 3% for the first time .
The latest moves will have added to the pool of euro zone bonds carrying sub-zero yields. This amounted to 3.71 trillion euros by close of trade on Thursday, according to Tradeweb, a sharp rise from 3.44 trillion in April.
Worldwide, analysts reckon more than $10.5 trillion in bonds now carry negative yields.
"We have to repeat the old saying that the trend is your friend," said DZ Bank strategist Christian Lenk.
U.S. Treasury yields are not in negative territory but they too resumed their slide, with 10-year yields falling to new 20-month lows. They are down around 34 bps this month and set for the biggest monthly fall since June 2016.
The U.S. yield curve, as measured in the gap between three-month and 10-year bond yields , was at its most inverted since 2007 in a sign of growing investor concern about recession risks.
But elsewhere in the euro zone, Italian yields jumped in response to the selloff in riskier assets, and growing concerns about the policies of the government in Rome.
Two-year Italian yields soared 15 bps to 0.80%, while the 10-year Italian/German bond yield gap was at its widest since December.
The Bank of Italy warned on Friday that public debt could rise more than forecast by the government in relation to domestic output this year, and called for measures to cut Rome's 2.3 trillion euro ($2.6 trillion) debt pile.
Global stock markets are feeling the pain as investors fled for the safety of bonds. European equity markets tumbled over 1% and U.S. stock futures pointed to a sharply lower open on Wall Street.
(Reporting by Dhara Ranasinghe and Virginia Furness, Editing by Susan Fenton and Ros Russell)