* Shares slip from Monday's record or multi-year highs
* Euro gains after inflation data not worse than expected
* Brent slips toward $108 as weak refining demand bites (Adds close of European stock, bond trading)
By Herbert Lash
NEW YORK, June 3 (Reuters) - Global equity markets slipped 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. Bond yields moved higher.
MSCI's all-country world index of equity performance in 45 countries fell 0.1 percent, while the pan-European FTSE Eurofirst 300 index of regional shares fell 0.41 percent to a provisional close of 1,374.78.
"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 25.62 points, or 0.15 percent, at 16,718.01. The Standard & Poor's 500 Index was down 2.29 points, or 0.12 percent, at 1,922.68. The Nasdaq Composite Index was down 9.10 points, or 0.21 percent, at 4,228.10.
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 0.21 percent to 1.3623 against the dollar as traders believe its recent weakness fully prices in an aggressive European Central Bank interest rate cut on Thursday.
The rate of euro zone inflation fell 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.
However, with most speculators already running big bets against the euro, traders said, even the weak figure was not enough to take the euro lower.
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 8/32 in price to yield 2.5626 percent.
German 10-year yields, the benchmark for euro zone borrowing, rose to 1.361 percent.
Brent crude oil futures slipped toward $108 a barrel, reflecting weak European refining demand. Brent futures for July were down 27 cents at $108.56 a barrel. U.S. crude was down 6 cents at $102.41 a barrel. (Reporting by Herbert Lash; Additional reporting by Nigel Stephensen; Editing by Chizu Nomiyama and Dan Grebler)