* STOXX 600 up 0.4 pct
* Autos jump after report of U.S. offer to suspend tariffs threat
* Miners and tech companies also rise
* Sodexo advances after sales update (Adds closing prices)
By Kit Rees
LONDON, July 5 (Reuters) - European shares gained a boost on Thursday as hopes of a softening in U.S. trade rhetoric lifted the car sector, though trading remained cautious ahead of a U.S. deadline to impose tariffs on Chinese goods.
The pan-European STOXX 600 index closed with a 0.4 percent gain for its third straight positive session. Germany's exporter-heavy DAX, meanwhile, was helped driven 1.2 percent higher by its carmakers.
European stocks have traded in a narrow range this week in anticipation of U.S. tariffs on $34 billion of Chinese imports from Friday.
Sectors that have been hardest hit by the uncertainty over the trade rift made some headway on Thursday, with autos jumping 3.4 percent and basic resources rising 1.4 percent.
Germany's BMW, Daimler, Porsche and Volkswagen were among the biggest STOXX risers, closing up as much as 4 percent after a report about a U.S. offer to suspend threats to impose tariffs on cars imported from the European Union.
"Now is a good time to make a few value plays under the assumption that these trade tariffs might not actually come to fruition," said Vertex Capital analyst Jasper Reimers.
Shares in carmakers have struggled in 2018 and remain 7.8 percent down for the year, among the worst-performing sectors in Europe.
Europe's technology sector, which came under pressure in the previous session after a Chinese court banned U.S. company Micron from selling some of its chips in China, regained ground with a 1.2 percent rise.
Elsewhere, company updates were in focus. Shares in France's Sodexo were the biggest STOXX 600 gainers, up 8.7 percent after the food services and facilities management group maintained its full-year goals despite posting slower third-quarter sales growth.
SBM Offshore was the biggest faller, down 7.2 percent after a Brazilian court ordered Petrobras to provisionally withhold some payments to SBM to ensure the Dutch company paid whatever penalties it received in a corruption case. (Reporting by Kit Rees and Julien Ponthus Editing by Alison Williams and David Goodman)