(Adds oil, gold settlement prices, European market close, graphics links)
* Apple hits record high in broad stock market advance
* U.S. bond yields fall on soft CPI data for April
* Dollar slips after U.S. CPI misses economist forecasts
By Herbert Lash
NEW YORK, May 10 (Reuters) - The dollar and U.S. government debt yields fell on Thursday while equity markets rallied after a modest rise in consumer prices in April eased concerns the Federal Reserve might raise interest rates more than expected this year.
The U.S. Labor Department said its Consumer Price Index rose 0.2 percent last month, less than forecasts for 0.3 percent, as a moderation in healthcare prices offset increases in the cost of gasoline and rental accommodations.
The dollar fell against the euro, the Japanese yen and a basket of other major currencies, while the Mexican peso and Brazilian real jumped more than 1 percent on the news.
Equity markets rose as the soft inflation data reduced the prospect of the Fed boosting rates three more times in 2018, instead of four times many in the market were forecasting.
Apple hit a record high at $190.37, with all 11 major S&P sectors posting gains.
Benchmark 10-year U.S. Treasury notes rose 8/32 in price to push yields down to 2.964 percent after breaching 3 percent on Wednesday.
"Inflation is going to rise in year-over-year terms over the summer, but the rise remains moderate rather than sharp," said Eric Winograd, senior economist at AllianceBernstein LP.
The soft read on inflation should give the Fed comfort that their gradual approach to raising rates is the correct one and ease market concerns, he said.
"I view today's number as a slight positive for risk assets in the near term," Winograd said.
However, the broad-based Underlying Inflation Gauge released by staff at the New York Fed later in the session showed inflation at 3.2 percent in April.
"We did have a miss on CPI for this particular month, but I don't think the overall trend for higher inflation has materially changed," said Eddy Vataru, a portfolio manager at Osterweis Capital Management in San Francisco.
"With oil prices north of $70, it's hard for me to believe this is going to be a persistent trend of inflation misses," he said.
MSCI's broad gauge of global equity markets rose 0.82 percent and turned positive for the year as it hit three-weeks highs.
Apple, Chinese internet giant Tencent, Microsoft and Facebook led the index's advance, while the U.S. technology sector lifted Wall Street.
Emerging market stocks rose 1.43 percent, after Asia-Pacific shares outside Japan and the Nikkei in Tokyo both earlier closed higher.
The pan-European FTSEurofirst 300 index of leading regional shares closed down 0.13 percent, but markets in London , Germany and France closed higher.
On Wall Street, the Dow Jones Industrial Average rose 197.78 points, or 0.81 percent, to 24,740.32. The S&P 500 gained 23.12 points, or 0.86 percent, to 2,720.91 and the Nasdaq Composite added 56.36 points, or 0.77 percent, to 7,396.27.
Oil markets were choppy but settled higher as traders eyed further declines in Venezuelan crude production in tandem with bullish drawdowns in U.S. crude inventories.
Brent crude futures rose 26 cents to settle at $77.47 a barrel, after hitting $78 earlier in the day, their highest since November 2014.
U.S. West Texas Intermediate crude futures settled up 22 cents at $71.36.
Gold rose on the weaker dollar and as tensions between the United States and Iran also supported the precious metal.
U.S. gold futures for June delivery settled up $9.30 at $1,322.30 per ounce.
Reporting by Herbert Lash; Editing by Bernadette Baum and Nick Zieminski