(Updates with U.S. markets' closing levels)
* MSCI global stock index eases
* Copper rises amid wage talks at world's largest mine
* Oil prices end higher
By Caroline Valetkevitch
NEW YORK, June 5 (Reuters) - The Nasdaq hit a record closing high for the second day in a row on Tuesday, helped by tech and consumer discretionary shares, while the euro recovered after Italy's new prime minister said the government had never considered leaving the euro zone.
Shares of Amazon AMZN.O , Apple AAPL.O and Netflix NFLX.O all rose. Upbeat economic data also helped the S&P 500 eke out a small gain. gains in equities were limited by worries about trade discussions. White House economic adviser Larry Kudlow said President Donald Trump may seek separate talks with Canada and Mexico in a bid to get individual trade deals with the two countries.
Mexico responded to Trump's metals tariffs by imposing its own duties on American steel, while also targeting agricultural products from pork to bourbon. administration imposed tariffs of 25 percent on imported steel and 10 percent on aluminum in March, citing national security grounds.
The market "continues to focus on one of two big issues - where we're headed with the trade negotiations - NAFTA, China and tariffs with Europe. That's probably the biggest concern for investors. But, on the positive side, (are) the economy's strength and earnings' strength," said Rick Meckler, partner at Cherry Lane Investments, a family investment office in New Vernon, New Jersey.
The U.S. services sector activity accelerated in May, pointing to robust economic growth in the second quarter. Dow Jones Industrial Average .DJI fell 13.71 points, or 0.06 percent, to 24,799.98, the S&P 500 .SPX gained 1.93 points, or 0.07 percent, to 2,748.8 and the Nasdaq Composite .IXIC added 31.40 points, or 0.41 percent, to 7,637.86.
MSCI's gauge of stocks across the globe .MIWD00000PUS shed 0.13 percent, while the pan-European FTSEurofirst 300 index .FTEU3 lost 0.32 percent.
CONTE'S COMMENTS
Comments by Italian Prime Minister Giuseppe Conte caused the dollar to fall and reverse gains to a near six-month high, as the euro recovered. euro rose 0.1 percent against the dollar to $1.1712 EUR= . The dollar index .DXY , tracking it against a basket of major currencies, fell 0.15 percent.
The Mexican peso MXN= gained 0.10 percent versus the U.S. dollar at 20.43. The Canadian dollar CAD=D4 rose 0.01 percent versus the greenback at 1.30 per dollar.
Earlier, the Mexican peso and Canadian dollar fell against the dollar as the latest developments in the growing trade conflict between the United States and its neighbors prompted selling in the currencies. Treasury yields fell as traders piled back into lower-risk government debt, however, after Conte vowed to enact economic policies that could add to the nation's debt load.
Benchmark 10-year U.S. Treasury notes US10YT=RR last rose 3/32 in price to yield 2.9259 percent, from 2.937 percent late on Monday.
Copper hit a six-week high as concerns about the potential supply impact of wage negotiations at the world's biggest copper mine helped push prices back above $7,000 a tonne. CMCU3 rose 2.04 percent to $7,117.00 a tonne.
Oil prices ended higher. U.S. crude CLcv1 rose 77 cents to settle at $65.52 a barrel, while Brent LCOcv1 gained 9 cents to settle at $75.38. Reuters Live Markets blog on European and UK stock markets open a news window on Reuters Eikon by pressing F9 and type in 'Live Markets' in the search bar