(Updates at settle)
* FTSEurofirst 300 down 0.7 pct as crude hits new lows
* Auto stocks rally as cheaper fuel boosts U.S. car sales
* Greek political outlook a concern
By Francesco Canepa and Sudip Kar-Gupta
LONDON, Jan 6 (Reuters) - European shares surrendered to a late selloff on Tuesday to end a choppy session lower as a renewed slide in crude prices and worries about Greece's Jan. 25 election unnerved investors.
Stocks yielded their gains as Brent crude fell to fresh 5-1/2 year lows just above $51 a barrel on growing worries over a global supply glut after top exporter Saudi Arabia gave no sign that it would cut output.
Oil majors such as Total, which had helped support the market, turned lower before the closing bell and explorers such as Ophir fell as much as 3.6 percent.
"It never looked like a complete turnaround, just a little bit of profit-taking (on negative bets) and off we go again," said Brenda Kelly, a strategist at IG.
On the flipside, lower energy costs helped to fuel strong auto sales in the United States in December, data showed late on Monday. This sent shares Fiat Chrysler Automobiles, the most exposed Europe-listed manufacturer, up 1.6 percent.
"Whenever you see an asset class fall as sharply as oil did, it tends to unnerve people and that does have consequences, and you see that in Russia," said Paul Sedgwick, head of investment at Frank Investments.
"But looking over history, a fall in oil prices boosts global growth. Oil will find a level, consumers will feel more confident and that will eventually feed through."
The broad FTSEurofirst 300 index of pan-European shares closed down 0.7 percent at 1,323.47 points after trading as high as 1,341.34 and as low as 1,319.84 points earlier in the day.
This took its loss since the start of the week to 2.9 percent.
Appetite for risk wilted amid uncertainty over the parliamentary election in Greece, which has revived a debate about whether the heavily-indebted country could leave the euro zone.
Traders cited a report by think-tank Oxford Economics which, based on an analysis of recent opinion polls, said the Greek left-wing Syriza party was on course to win a "clear mandate" to implement anti-austerity policies that are inconsistent with the country's euro membership. (www.oxfordeconomics.com)
"I don't think they will push Greece out of the euro zone, but just the sheer mention of this being a possibility is making investors nervous," said Darren Courtney-Cook, head of trading at Central Markets Investment Management.
Europe bourses in 2014: link.reuters.com/pap87v
Asset performance in 2014: link.reuters.com/gap87v
Today's European research round-up (Reporting By Francesco Canepa; Editing by Gareth Jones)