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UPDATE 1-Investors grab top-rated bonds as stocks tumble on Trump doubts

* Demand for "safe haven" bonds rises as stocks wobble

* Concern over Trump's ability to pass economic plan

* White House denies rumour Gary Cohn quitting

* Barcelona van attack kills 13, wounds scores

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Retops, adds quote, updates prices)

LONDON, Aug 18 (Reuters) - Demand for highly-rated euro zone bonds increased on Friday as equity markets tumbled on mounting concerns that U.S. President Donald Trump faces difficulties in passing his economic agenda.

The yield on Germany's benchmark government bond fell as much as 3 basis points to just below 0.40 percent, and U.S. equivalents matched a six-week low of 2.182 percent .

Meanwhile, yields rose slightly on southern European bonds in the likes of Spain and Portugal in a global retreat from riskier assets that saw the biggest drop in three months on Wall Street overnight.

"We have seen the first wobble in equities for some time now, with the S&P closing down 1.5 percent last night, so there's a bit of a risk-off safe haven bid for bonds at the moment," said Daniel Loughney, portfolio manager at AllianceBernstein.

Concerns have grown too over Trump's ability to push through his economic goals such as tax cuts and infrastructure spending, following the exodus of executives from two prominent business councils in reaction to his response to clashes last weekend in Charlottesville, Virginia.

Trump on Thursday decried the removal of pro-slavery Civil War Confederacy monuments, which have fuelled U.S. racial tensions, stoking worries that some of his key policy staffers and aides may quit.

Chief among them were rumours that Gary Cohn, director of the National Economic Council, would resign. The White House denied those rumours.

"Those rumours are in our view the embodiment of the market's nervousness," Mizuho strategist Peter Chatwell said.

The caution in markets was compounded by a deadly attack by a suspected Islamist militant in Barcelona.

Spain mounted a sweeping anti-terror operation on Friday after the suspected Islamist militant drove a van into crowds on a popular tourist thoroughfare in Barcelona, killing 13 people before fleeing, in what police suspect was one of multiple planned attacks.

The death toll could rise because more than 100 are injured, authorities said. Similar attacks have killed well over 100 people in Nice, Berlin, London and Stockholm.

The fall in yields extended a move that started earlier in the week after minutes from U.S. Federal Reserve and European Central Bank meetings showed policymakers were cautious about withdrawing monetary stimulus too quickly.

Dallas Fed President Robert Kaplan on Thursday said the Fed should be "very patient and judicious" as it considers whether to raise interest rates.

Later on Friday, Greece's credit rating will be reviewed by Fitch. Greece is rated CCC by Fitch and analysts at DZ Bank said the country may get as much as a two-notch upgrade back into B territory.

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s

(Editing by Matthew Mpoke Bigg)