* Trump menaces Mexico with tariffs in surprise tweet
* Markets see recession risk, price in deeper Fed rate cuts
* China PMI disappoints with drop to 49.4 in May
* Europe stocks tumble, U.S> futures in the red
* Bonds jump on safe-haven rush, U.S. yields at fresh lows
By Karin Strohecker
LONDON, May 31 (Reuters) - European stocks tumble and sovereign bonds surged on Friday as investors feared President Donald Trump's shock threat of tariffs on Mexico risked tipping the United States into recession while disappointing China data added to the woes.
Markets moved aggressively to price in deeper rate cuts by the Federal Reserve this year, while U.S. bond yields touched fresh lows and parts of the curve inverted further, seen as a warning signal for recession in the world's largest economy.
Washington will impose a 5% tariff from June 10, which would then rise steadily to 25% until illegal immigration across the southern border was stopped. Trump announced the decision on Twitter late Thursday, catching markets completely by surprise.
"Very clearly when we all though that the main trade tensions in the world were between the U.S. and China or perhaps between the U.S. and Europe, we hadn't realised there will be another trade tension with Mexico...and it raises concerns about who the next country may be," said Andrew Milligan, head of global strategy at Aberdeen Standard Investments.
The investor mood darkened further when a key measure of Chinese manufacturing activity for May disappointed, raising questions about the effectiveness of Beijing's stimulus steps. This also sparked concerns over the health of the global economy more widely.
"It is a nasty slowdown, it looks likely to be taking longer than we thought. Many thought that the slow down would be in Q1 and the recovery in Q2, but clearly everything that we see in May is telling us this will be pushed back into Q3 or Q4," Milligan added.
Yields on the 10-year Treasury note quickly fell to a fresh 20-month low of 2.17%, while the dollar jumped more than 3% on the Mexican peso.
In Europe, the pan-European STOXX 600 dropped 1%, slumping to a more than three-month low with the trade sensitive German DAX down 1.4%. All sectors were in the red, though the falls were led by carmakers which dropped more than 2% while Volkswagen and Fiat Chrysler - both having significant exposure to Mexico - dropped 4%.
Spanish banks exposed to Mexico - Santander, Sabadell and Bilbao - also suffered.
Wall Street - on track for the first monthly decline of 2019 - looked also in line for sizeable falls, with e-Mini futures for the S&P 500 pointed to a 1% lower open.
Asian shares fell at first, but some drew month-end bargain hunting having endured a torrid few weeks. MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.2%, but is still down a whopping 7.4% for the month.
China's blue chip index closed a touch lower on hopes Beijing would now have to ramp up its stimulus containing losses. Japan's Nikkei dropped 1.6%, dragged down by big falls in car makers, and down 7.1% on the month. Investors clearly reckoned that opening a new front in the trade wars would pressure central banks everywhere to consider new stimulus. On Thursday, Federal Reserve Board of Governors Vice Chair Richard Clarida had said the central bank would act if inflation stays too low or global and financial risks endanger the economic outlook.
"What the Clarida's comments have done is clarify in many people's minds the answer to the questions of whether low inflation proving more than transitory would itself be enough to get the Fed to ease – the answer appears to be 'yes'," said Ray Attrill, head of FX strategy at National Australia Bank.
"That served to reinforce prevailing market expectations that the Fed will be easing in the second half of this year."
Indeed, the case that the inflation slowdown was temporary took a blow when the core personal consumption expenditures index, the Fed's favoured measure of inflation, was revised down to 1% for the first quarter, from 1.3%.
Trump's tariff threat only added to the dangers and the market further narrowed the odds on Fed easing this year and next. Futures imply no less than 44 basis points of cuts by year end in the current effective funds rate of 2.38%.
Bonds extended their bull run with 10-year Treasury yields now down a steep 33 basis points for the month and decisively below the overnight funds rate. US 3-month yields were some 20 basis points above those on 10-year Treasury bonds, the biggest inversion since 2007.
Such an inversion of the yield curve has presaged enough recessions in the past that investors are wagering the Fed will be forced to ease policy just as "insurance".
Yet Treasuries are hardly alone in rallying, with Germany's benchmark 10-year bond yield flirting with fresh record lows.
In currency markets, the dollar suffered the biggest one day fall against the safe haven Japanese yen since March at 0.7%. Against a basket of currencies, the dollar pulled 0.2% lower to trade at 97.975.
The euro also fell sharply against the Japanese yen and was down nearly 0.5% at 121.34 after touching the lowest since a Jan. 3 flash crash.
China's yuan is set for its worst month since July last year and was heading towards the crucial 7 per dollar figure. Sterling was poised for the biggest monthly drop in a year as the imminent departure of Theresa May as prime minister deepened fears about a chaotic divorce from the European Union.
In commodity markets, spot gold firmed 0.4% to $1,293.33 per ounce. Oil prices fell to a near-three month low on fears a global economic slowdown would crimp demand. U.S. crude was last down 57 cents at $56.02 a barrel, while Brent crude futures lost 95 cents to $65.92.
Reporting by Karin Strohecker, additional reporting by Wayne Cole in Sydney