* Wall Street mostly flat
* Oil jumps past $80 per barrel
* European shares near four-month peak, Italy bond selloff relents
* Dollar eases off highs while gold steadies (Updates to afternoon trading)
By Laila Kearney
New York, May 22 (Reuters) - World stock markets were little changed on Tuesday as Wall Street investors locked in recent gains even as European shares approached four-month peaks and China moved to further open up its economy.
Washington neared an agreement to lift its ban on U.S. firms supplying to Chinese telecoms gear maker ZTE Corp, sources said, while Beijing said it would steeply cut import tariffs for automobiles and car parts.
That boosted shares of U.S. auto makers Ford, General Motors, and U.S.-listed shares of Fiat.
Europe's big carmakers Volkswagen, BMW , Daimler jumped, too.
More broadly, world stock markets were mixed as investors took profit from the previous session's rally supported by a U.S.-China trade war truce. MSCI's gauge of stocks across the globe gained 0.21 percent.
The U.S. consumer discretionary index fell 0.2 percent on disappointing reports from retailer Kohl's and homebuilder Toll Brothers, but analysts paid the reports little notice.
"I don't think today there is any news that's particularly concerning other than disappointing guidance from Kohl's and disappointing results from Toll Brothers," said Michael James, managing director of equity trading at Wedbush Securities in Los Angeles. "I don't think it's anything other than some profit taking."
On Wall Street, the Dow Jones Industrial Average fell 67.75 points, or 0.27 percent, to 24,945.54, the S&P 500 gained 1.93 points, or 0.07 percent, to 2,734.94 and the Nasdaq Composite added 6.68 points, or 0.09 percent, to 7,400.71.lost 0.18
European shares were up as Italian government bond yields slipped from multi-month highs after six days of steep selling tied to the growing likelihood of a government comprised of the anti-establishment 5-Star Movement and the far-right League.
Analysts said the price falls of recent days might render the debt attractive again for some.
The pan-European FTSEurofirst 300 index rose 0.29 percent.
Meanwhile, oil prices jumped past the world benchmark of $80 a barrel to its highest since late 2014, on mounting supply concerns tied to Venezuelan crude output and a possible cut in Iranian exports that could further curb global supply.
The concerns were exacerbated when Washington added fresh sanctions against Venezuela following President Nicolas Maduro's disputed re-election over the weekend.
After six days of gains, the U.S. dollar retreated as Treasury yields dipped and investors sought incentives to buy after a 7 percent rally since mid-February.
The dollar's recent uptrend has been supported by generally upbeat U.S. economic data that has kept the Federal Reserve on track to raise interest rates at least two more times this year.
The dollar index fell 0.06 percent, with the euro down 0.13 percent to $1.1775.
Gold steadied as the dollar lost momentum, but risk appetite in the broader financial market cooled the metal's gains.
U.S. gold futures gained 0.06 percent to $1,291.70 an ounce.
Additional reporting by Marc Jones, Alex Lawler, Gertrude Chavez-Dreyfuss, Maytaal Angel and Stephanie Kelly; Editing by Bernadette Baum