* S&P 500, Nasdaq turn negative
* Facebook, Alphabet drag down tech stocks
* Twitter falls after short-seller report
* Dow up 0.13 pct, S&P down 0.34 pct, Nasdaq off 1.42 pct (Updates to late afternoon, changes byline)
By Stephen Culp
March 27 (Reuters) - Wall Street gave up gains on Tuesday with technology stocks pulling the S&P 500 and the Nasdaq into negative territory.
Stocks seesawed earlier in the session on the heels of their best gains in 2-1/2 years on Monday as trade war fears eased.
White House trade adviser Peter Navarro confirmed on Monday that top Trump administration officials have asked China to cut tariffs on imported cars, allow foreign majority ownership of financial services firms and buy more U.S.-made semiconductors in negotiations to avoid imposing tariffs on a host of Chinese goods.
A person familiar with the discussions said these were among the asks from Treasury Secretary Steven Mnuchin and U.S. Trade Representative Robert Lighthizer as they pursue talks with Beijing.
"Trade is in the back of people's minds," said Robert Pavlik, chief investment strategist and senior portfolio manager at SlateStone Wealth in New York. "But show me the reality of this. I need to see a little proof before I really commit."
Early advances were dampened by the technology sector, which pulled the S&P 500 and the Nasdaq into negative territory as a scandal widened over political consultants' use of Facebook user data.
"Nobody's really sure what impact the government is going to impose on their business model. I think it's a lot of chest pounding on the part of regulators and other parties that are trying to make political hay out of it," said Pavlik.
Last week was Wall Street's worst since January 2016, slammed by news that President Donald Trump would impose tariffs of up to $60 billion on Chinese imports.
But the markets roared back on Monday with their best day since August 2015 on hopes that the world's two largest economies were willing to renegotiate tariffs and trade imbalances.
At 2:37PM ET, the Dow Jones Industrial Average rose 27.1 points, or 0.11 percent, to 24,229.7, the S&P 500 lost 9.08 points, or 0.34 percent, to 2,649.47 and the Nasdaq Composite dropped 101.56 points, or 1.41 percent, to 7,118.99.
Of the 11 major sectors of the S&P 500, three had turned negative by mid-afternoon, led by a 1.7 percent decline in technology stocks.
Facebook led technology stocks lower, down 4 percent as the scandal over the use of data by political consultants widened after a whistleblower said Canadian company AggregateIQ had developed a program to target Republican voters in the 2016 U.S. election.
Alphabet shares fell 2.4 percent after an appeals courts resurrected a multibillion dollar copyright case brought by Oracle Corp against the tech giant.
Nvidia was another weak spot, falling 6.6 percent after the chipmaker temporarily suspended self-driving tests across the globe.
Tesla shares were off 6.4 percent after the U.S. National Transportation Safety Board opened a field investigation of last week's fatal Tesla crash and vehicle fire.
Twitter fell 9.1 percent after short-seller Citron Research called the stock "most vulnerable" to privacy regulations.
Declining issues outnumbered advancing ones on the NYSE by a 1.11-to-1 ratio; on Nasdaq, a 1.85-to-1 ratio favored decliners. (Reporting by Stephen Culp; Editing by Cynthia Osterman)