* Shares slip from previous day's record or multi-year highs
Euro gains after inflation data not worse than expected
* Brent slips towards $108 as weak refining demand bites
(Adds opening of U.S. markets, byline, dateline; previous LONDON)
By Herbert Lash
NEW YORK, June 3 (Reuters) - Global equity markets slid on Tuesday from record or multi-year highs, while euro zone inflation data gave the euro some respite on relief that price growth in the single currency zone had not slowed even further.
Stocks on Wall Street were lower, following declines across Europe, but emerging market stocks rose, lifted in part by rising Brazilian and Mexican shares.
MSCI's all-country world index of equity performance in 45 countries, fell 0.03 percent, while the pan-European FTSE Eurofirst 300 index of regional shares fell 0.4 percent to 1,374.98.
"Valuations are elevated, and therefore anything that looks soft gives the market pause," said Mark Luschini, chief investment strategist at Janney Montgomery Scott in Philadelphia.
The Dow Jones industrial average fell 31.03 points, or 0.19 percent, to 16,712.6. The S&P 500 lost 2.21 points, or 0.11 percent, to 1,922.76 and the Nasdaq Composite dropped 1.315 points, or 0.03 percent, to 4,235.884.
Both the S&P 500 and Dow industrials closed at record highs on Monday, while MSCI's gauge of global equities closed at more than a six-year high, about 1.4 percent away from all-time highs set in late 2007.
The euro rose 0.31 percent to 1.3636 against the dollar as traders said expectations the European Central Bank would cut interest rates on Thursday were already largely priced in and that only a weaker inflation number would have triggered a big market move.
Euro zone inflation fell unexpectedly in May, increasing the risks of deflation, as core inflation, excluding energy, food, alcohol and tobacco, fell to 0.7 percent from 1.0 percent in April.
With most speculators already running big bets against the euro, traders said, only a weaker-than-expected inflation reading of 0.4 percent or lower would have taken the euro towards $1.3580 - levels last seen in mid-February.
U.S. Treasuries yields rose to their highest in three weeks as investors reset bets that yields are likely to rise, after they fell to 11-month lows last week.
German bund yields spiked after euro zone inflation was in-line with revised expectations, prompting some in the market who had expected an even weaker number to book profits after a recent rally.
Benchmark 10-year notes were last down 10/32 in price to yield 2.5697 percent.
German 10-year yields, the benchmark for euro zone borrowing, rose to 1.368 percent.
Brent crude oil futures slipped towards $108 a barrel, reflecting weak European refining demand.
Brent futures for July were down 37 cents at $108.46 a barrel. U.S. crude was down 5 cents at $102.42 a barrel.
(Additional reporting by Nigel Stephensen, reporting by Herbert Lash; Editing by Chizu Nomiyama)