* U.S. agrees to refrain from car tariffs on EU for now
* World stock index hits highest since mid-March
* European auto sector jumps 2 pct, European stocks up
* Chinese stocks still suffer as concerns persist
* Graphic: World FX rates in 2018 tmsnrt.rs/2egbfVh
By Abhinav Ramnarayan
LONDON, July 26 (Reuters) - European stocks opened much higher on Thursday, pushing world stocks to new four-month highs after the European Union and the United States agreed to negotiate on trade, easing some of the fears of a transatlantic trade war.
Concerns over the slowing pace of world economic growth and some lacklustre company earnings reports capped some of equity gains, however, as did lingering fears that Washington's trade tensions with China could escalate further.
In what the EU chief called a "major concession," U.S. President Donald Trump agreed on Wednesday to refrain from imposing car tariffs while the two sides launch negotiations to cut other trade barriers.
There were gains across the board for European stocks on Thursday morning, led by the continent's auto sector, which was up 2 percent at one point German's export-reliant and auto-heavy index rose 1.4 percent
A pan-European stock index rose half a percent while the MSCI world equity index, which tracks shares in 47 countries, hit its highest since March 16 on the news.
"The lifting of the threat of tariffs on the auto sector in particular is a major development. We've not seen a lot of actual measures implemented but it should lift the confidence of manufacturers," said RBC European economist Cathal Kennedy.
"The feedthrough should come through in the manufacturing sector and confidence indicators in the coming months."
The equity gains pushed up government bond yields in the U.S. and Europe, with Germany's 10-year yield, the benchmark for the euro zone, coming close to a one-month high at 0.42 percent.
There were clouds on the horizon, however.
Asian stocks were held back by weakness in China, where the Shanghai Composite index fell 0.7 percent and blue-chip shares lost 1.1 percent. This capped gains for MSCI's broadest index of Asia-Pacific shares outside Japan to just 0.1 percent.
While the transatlantic mood was improving, "this deal, along with the breakdown of a large M&A deal, leave investors fearing that the trade war has just turned even more so on China," Citi analysts told clients.
They were referring to the likelihood that Qualcomm Inc would drop its $44 billion bid for NXP Semiconductors NXPI.O after a deadline for securing Chinese regulatory approval passed.
Economic growth worries are also mounting -- economists polled by Reuters said global activity had peaked, with trade protectionism seen having a significant downward impact . Thursday's South Korean data showing slowing growth and exports reinforced that picture.
Another poll indicated U.S. second quarter growth -- with data due on Friday -- also would mark the peak.
Trade and growth worries were already taking a toll on some companies' bottom lines.
U.S. automakers General Motors, Ford Motor and Fiat Chrysler Automobiles have cut profit forecasts, while Germany's Daimler blamed U.S.-China tariffs for a 30 percent drop in second-quarter profit.
A warning of slowing growth from Facebook Inc, which saw the company's stock fall as much as 24 percent in after-hours trading on Wednesday, highlighted risks for investors and businesses in the current earnings season.
That is likely to weigh on Wall Street at open, with S&P500 futures down 0.2 percent
Focus will now turn back to central bank policy and the softer U.S.-EU tone should help the European Central Bank stick with its plan to gradually withdraw stimulus when it meets later on Thursday.
The euro, having strengthened on Wednesday on the news, held on to its gains against the dollar and was at $1.1731 while the dollar was down 0.20 percent against a basket of currencies.
The yen fell 0.3 percent against the dollar but investors will carefully watch the Bank of Japan's two-day policy review on July 30-31 after this week's brief jump in yields and the Japanese currency on reports authorities were debating paring back some stimulus.
The bank is said to be considering changing the composition of exchange-traded funds it buys as part of its stimulus programme.
Brent crude meanwhile was up over a percent to hit a 10-day high of $74.68 per barrel Brent crude led oil prices higher, extending gains into a third day after Saudi Arabia suspended crude shipments through a strategic Red Sea shipping lane.
For Reuters Live Markets blog on European and UK stock markets open a news window on Reuters Eikon by pressing F9 and type in 'Live Markets' in the search bar (Reporting by Abhinav Ramnarayan, Additional reporting by Andrew Galbraith in SHANGHAI; Editing by Hugh Lawson)