By Saqib Iqbal Ahmed

NEW YORK (Reuters) - Stocks gained broadly on Tuesday, helped by buoyant oil prices, a day after Federal Reserve Chair Janet Yellen pushed back expectations for an interest rate increase without raising concerns over the strength of the world's largest economy.

Crude oil futures traded above the psychologically important $50 mark, touching a 2016 high, supported by a weaker U.S. dollar, which wallowed near a four-week low.

The MSCI world equity index <.MIWD00000PUS>, which tracks shares in 45 nations, rose to the highest in more than six weeks.

"It's all related. Oil is moving higher on the diminished threat of higher rates," said Jack Ablin, chief investment officer at BMO Private Bank in Chicago.

Higher interest rates boost the U.S. dollar, which in turn hurts dollar-denominated commodity prices.

Worries over potential supply shortages from attacks on Nigeria's oil industry helped boost oil prices, as did expectations of a likely drop in U.S. crude stocks, a third decline in as many weeks.

"With the industry projecting a decline in total U.S. crude oil stocks in this week's reports, the market bears are remaining on the sidelines," said Dominick Chirichella, senior partner at the Energy Management Institute in New York.

The price of oil has nearly doubled since January, boosted largely by a spate of unplanned outages that have eroded production in Canada, Venezuela, Libya and Nigeria, along with a steady decline in higher-cost U.S. shale output.

Strength in energy shares pushed the S&P 500 index <.SPX> to within 16 points of its record high, while the Dow Jones industrial average <.DJI> climbed above 18,000 for the first time since April. Chevron <CVX.N> rose 2.5 percent and Exxon <XOM.N> gained as much as 1.8 percent to a 52-week high of $90.91.

The Dow Jones industrial average <.DJI> rose 17.95 points, or 0.1 percent, to close at 17,938.28, the S&P 500 <.SPX> gained 2.72 points, or 0.13 percent, to 2,112.13, while the Nasdaq Composite <.IXIC> dropped 6.96 points, or 0.14 percent, to 4,961.75.

Europe's broad FTSEurofirst 300 index <.FTEU3> closed up 1.19 percent at 1,360.25, taking cues from Yellen's remarks on Monday and helped by improving sentiment due to the firmer oil prices.

The MSCI world equity index <.MIWD00000PUS> was up 0.61 percent, its fourth session of gains.

In the currency market, the Australian dollar <AUD=D4> was the biggest gainer among major currencies after the Reserve Bank of Australia kept interest rates on hold and hinted it was in no hurry to ease monetary policy further on signs of reasonably strong economic growth.

The U.S. dollar hovered near four-week lows against a basket of currencies as traders speculated when the Fed may next raise interest rates. The dollar index <.DXY> was last down 0.02 percent at 93.887.

In the bond market, U.S. Treasury prices rose, boosted by expectations the Fed will not raise interest rates for several months. But they briefly pared gains after the government had to pay more to sell new notes.

The Treasury sold $24 billion in three-year notes at a high yield of 0.93 percent, around half a basis point above where the notes had traded before the auction.

Benchmark 10-year notes <US10YT=RR> gained 3/32 in price to yield 1.713 percent, down from 1.723 percent late on Monday. The yields have risen from two-month lows of 1.697 percent hit on Friday.

Brent crude <LCOc1> settled up 89 cents, or 1.76 percent at $51.44 a barrel, while U.S. crude <CLc1> settled up 67 cents, or 1.35 percent, at $50.36.

Gold eased as investors turned cautious after the metal failed to sustain a recent rally. Spot gold prices <XAU=> were down 0.1 percent to $1,243.57 an ounce, still near a 2-week high.

(Additional reporting by Chuck Mikolajczak and Barani Krishnanin New York; Editing by Nick Zieminski and Dan Grebler)