* FTSEurofirst 300 down 0.4 pct
* Syngenta rises on BASF bid interest
* Europe bourses in 2015: link.reuters.com/pap87v
* Asset performance in 2015: link.reuters.com/gap87v
By Francesco Canepa and Sudip Kar-Gupta
LONDON, June 4 (Reuters) - European shares pared most of their daily losses on Thursday as a rally in the euro and bond yields paused, helped by some better-than-expected U.S. economic data.
The data showed the number of Americans filing new claims for unemployment benefits fell slightly more than expected last week.
That pointed to U.S. labour market resilience and lured buyers back into the dollar, pushing down the euro and thereby helping a recovery in euro zone shares and government bonds.
The FTSEurofirst 300 index was down 0.4 percent at 1,563.85 points at 1434 GMT, having earlier touched its lowest level since May 7.
The European Central Bank's insistence on Wednesday that there was no need to adjust monetary policy in the face of volatility had caused a spike in the euro and bond yields.
This cast a shadow on borrowing costs and export prospects for companies in the region.
"The pick-up in the bond yields is putting pressure on the European stock markets," said Mirabaud Securities' senior equity sales trader John Plassard.
The index rallied nearly 25 percent between mid-January and mid-April as the announcement of a bond-buying programme by the ECB knocked the single currency and lowered borrowing costs for European governments and companies, as well as boosting equities' attraction by lowering returns on bonds.
But over the past month the index has been at its most volatile since 2012, based on the size of the moves between its open, high, low and close.
Utilities, which had been seen as a natural replacement for bond investments due to their reliable dividend and higher yield versus bonds, were hit hardest, falling 2.2 percent.
Greece's benchmark ATG equity index closed 1.3 percent lower, giving back some of its gains in the previous day, as talks over the country's debt problems continued.
Greece's EU/IMF lenders have asked Athens to commit to selling off state assets, implement pension cuts and maintain unpopular labour reforms, sources familiar with their proposal said on Thursday. Such demands would cross the government's so-called red lines.
Greek Prime Minister Alexis Tsipras will brief parliament on on Friday, a government official said on Thursday.
"Clearly there remains some way to go in the talks so I refuse to get too optimistic. The messages coming from the talks are extremely mixed and even the creditors can't agree on a consistent stance," said OANDA senior market analyst Craig Erlam.
Swiss agrochemicals group Syngenta outperformed to rise 1.8 percent after Reuters reported that German company BASF was considering a bid.
Corporate takeover activity, as evidenced in the possible bid battle for Syngenta, has provided a cushion for European stock markets this year, in spite of worries over Greece.
In addition, some investors saw rising yields, a reflection of rising inflation expectations, as a sign the euro zone economy was recovering, pointing to a favourable backdrop for stocks.
Research by JP Morgan Asset Management showed there is a historically positive correlation between rising bond yields and positive equity returns when rates are moving up from a low base.
"Equities represent the best value and should continue to offer an attractive and growing income when compared to bonds, even if bond yields start to rise," said Stephen Thornber, manager of the St. James's Place strategic managed fund.
Today's European research round-up (Additional reporting by Lionel Laurent; Editing by Andrew Roche)