* Hopes of a U.S.-China deal on trade boost stocks
* Carmakers jump 1.6 percent
* Luxury stocks also driven by trade hopes
* European stocks pare gains through the day on U.S. jobs data
* STOXX 600 closes up 0.3 percent (Updates prices, adds details, quotes)
LONDON, Nov 2 (Reuters) - European shares had a third day of gains on Friday after U.S. President Donald Trump fueled hopes among investors that a deal to end a prolonged dispute over trade could be reached with his Chinese counterpart Xi Jinping later this month.
The pan-European STOXX 600 hit its highest since Oct. 10 in early deals and sealed its best week since Dec 2016, rising 3.4 percent on the week.
"With sentiment in both China and the U.S. damaged by trade tensions, it is unsurprising that even a hint of incremental progress is enough to lift markets," wrote UBS' Chief Investment office, adding however that their base case was for the trade dispute to worsen before it improves.
While stocks surged early in the session, they closed near the day's lows, weighed down by falls in U.S. stocks.
Strong jobs data from the U.S. dampened gains for European stocks and drove U.S. stocks into the red in afternoon trading, as the surge in wages added to signs of labour market tightening that could encourage the Fed to raise rates again in December.
Fears of a full-blown trade war, rising U.S. bond yields, slowing Chinese growth, political risk in the form of Brexit and Italy's populist government have all been blamed for last month's "red October" during which indexes worldwide sustained some of their worst losses since the 2008 financial crisis.
Germany's DAX climbed 0.6 percent, lifted by the big exporters among its constituents, such as car maker Volkswagen, up 4 percent.
Europe's autos index led gains, jumping 1.7 percent as signs of progress in trade talks boosted the sectors seen as most vulnerable.
Auto parts makers Faurecia, Valeo, and Plastic Omnium were among the best-performing in Europe, up 4.5 to 7.6 percent.
Trade-sensitive luxury stocks also rose. Boosted by an upgrade from Goldman Sachs, Gucci owner Kering topped the euro zone blue chip index with a 5.4 percent rise.
Other luxury stocks such as LVMH and Moncler also climbed 3.3 and 5.5 percent.
Europe's tech stocks rose 1 percent, shrugging off Apple's disappointing results which drove the iPhone maker's shares down 7 percent.
"Growth investors, technology investors, and the wider market was hoping for a positive steer from Apple that all was well in the world. And that didn't happen," wrote Neil Campling, co-head of the global thematic group at Mirabaud Securities.
Wirecard was a weak spot, down 6.5 percent at the bottom of the STOXX 600 after Bank of America Merrill Lynch analysts downgraded the stock to "underperform", saying competition for the payments platform is strong.
The banking sector was up 1.4 percent, with no evidence of angst about the results of European stress tests set to come out after the close.
Italian lenders are under the spotlight with their heavy exposure to sovereign Italian debt, which is suffering from the populist governments spending plans and its row with the EU's executive body.
Overall this earnings season has seen weak results from European companies.
Morgan Stanley strategists said recent results have improved from the very weak start to earnings season, but so far the third quarter continues to show the weakest EPS (earnings per share) in four years.
More broadly the sell-off hitting global developed market stocks has been regardless of still strong earnings expectations.
(Reporting by Julien Ponthus; Editing by Josephine Mason, Editing by William Maclean, Richard Balmforth)