* U.S. stocks climb in afternoon trading
* 10-year Treasury prices slip after Grassley comments on trade
* Oil slides; data shows surprise build in U.S. crude stockpiles (Updates with European markets close and U.S. oil settles lower)
By Caroline Valetkevitch
NEW YORK, June 5 (Reuters) - Major world stock markets rose and longer-dated U.S. Treasury prices dipped on Wednesday as a U.S. senator predicted the United States will not impose tariffs on Mexican imports, while hopes of a U.S. interest rate cut also bolstered equities.
Republican Senator Chuck Grassley predicted that the United States and Mexico would be able to strike a deal to avert tariffs U.S. President Donald Trump has threatened to impose on Mexican imports.
A flare-up in trade tensions between the United States and China hurt world stocks in May and triggered fears of an impending recession. Comments from Federal Reserve Chairman Jerome Powell and other Fed officials this week helped limit equity market losses as they warned the trade war may force them to respond, prompting investors to price in possible rate cuts.
"The Fed is clearly leaning in the direction that it will cut rates if it sees anymore slowing in the economy, and there is that hope that we can avoid putting tariffs on Mexico so that is a positive," said Art Hogan, chief market strategist at National Securities in New York.
Underscoring concerns over growth was a report by U.S. payrolls processor ADP Wednesday that showed U.S. private employers added 27,000 jobs in May, well below economists' expectations and the smallest monthly gain in more than nine years.
Interest rate futures show the U.S. central bank will start cutting rates as soon as next month, with as many as three rate cuts priced by year-end.
The Dow Jones Industrial Average rose 188.81 points, or 0.75%, to 25,520.99, the S&P 500 gained 19.74 points, or 0.70%, to 2,823.01 and the Nasdaq Composite added 37.11 points, or 0.49%, to 7,564.23.
MSCI's broad gauge of stocks across the globe was on track for a third day of gains, rising 0.6%. The pan-European STOXX 600 index rose 0.38%.
In the U.S. Treasuries market, benchmark 10-year notes last fell 3/32 in price to yield 2.1296%, from 2.121% late on Tuesday. Yields held above 2.061% reached on Monday, which was their lowest level since September 2017.
Earlier, Germany's 10-year bond yield reached a record low and Italian debt held on to this week's gains as investors ramped up their bets on a generous loan package for banks in the euro zone as well as a U.S. rate cut.
The U.S. dollar was higher in afternoon trading, reversing earlier losses.
The dollar index, which tracks the greenback versus a basket of six currencies, rose 0.21 points or 0.22 percent, to 97.282. The yen was last up 0.23 percent, at 108.3900 per dollar.
Oil prices resumed their recent slide, extending losses after data showing a surprise build in U.S. crude stockpiles.
U.S. crude fell 3.37% to settle at $51.68 a barrel.
Gold prices jumped to their highest in 15 weeks as the U.S. rate cut bets encouraged investors to flock toward bullion. Spot gold was up 0.3% to $1,329.41 per ounce.
Reporting by Caroline Valetkevitch; Additional reporting by Richard Leong in New York, Medha Singh in Bengaluru and Ritvik Carvalho in London; Editing by Bernadette Baum and Lisa Shumaker