* U.S. stocks fall, weighed by energy sector, BofA
* Oil sinks 1 percent on rising rig count figures
* U.S., European bond yields fall from highs (Updates to afternoon trading)
By Dion Rabouin
NEW YORK, Oct 17 (Reuters) - Major stock markets around the world fell on Monday and U.S. and European bond yields slipped off four-month highs amid uncertainty over the health of the global economy.
U.S. stocks fell as declining oil prices pushed energy stocks down and traders sold Bank of America shares despite a well-received earnings report from the country's second-largest bank by assets.
Stocks touched their lows of the day following comments from Federal Reserve Vice Chairman Stanley Fischer, who said economic stability could be threatened by low interest rates, but it was "not that simple" for the Fed to raise rates.
European stocks closed lower across the board with the pan-European FTSE Eurofirst 300 index down 0.69 percent.
"I think we're headed for a bumpy session with earnings leading the way," said Peter Cardillo, chief market economist at First Standard Financial in New York. "It's also a jittery market ahead of the elections and of course the prospects of a rate hike (by the U.S. Federal Reserve) in December."
The Dow Jones industrial average fell 60.36 points, or 0.33 percent, to 18,078.02, the S&P 500 lost 6.56 points, or 0.31 percent, to 2,126.42 and the Nasdaq Composite dropped 13.04 points, or 0.25 percent, to 5,201.12.
A gauge of equity markets around the globe was down 0.25 percent.
Oil fell around 1 percent as a rising U.S. rig count kept investors worried about a persisting glut. The energy sector led all S&P components lower, down 0.75 percent in early trading.
Brent crude futures were down just under 1 percent at $51.46, with U.S. crude futures at $49.73 per barrel, down 1.25 percent.
U.S. and European government bonds reversed earlier selling and rose in price after benchmark 10-year Treasury note yields hit their highest since June 2 and German and British bonds touched their highest since late June.
Buying in Treasuries was spurred by bargain-hunting investors who scooped up government debt that had fallen in price on Friday following remarks by Federal Reserve Chair Janet Yellen, analysts said. Yellen had said the central bank may tolerate inflation above its 2-percent goal.
The rise in prices also followed a sub-par reading from the New York Fed's gauge on regional business activity in October.
The 10-year U.S. Treasury note rose 7/32 in price to yield 1.766 percent, falling from a high of 1.814 percent.
British 10-year gilt yields were last at 1.126 percent, falling from 1.223 percent in European trading, the highest since June 20.
German 10-year bunds were last yielding 0.057 percent, falling from 0.104 percent, their highest since June 24.
The U.S. dollar retreated from a seven-month high as some investors took profit following a recent rally that received a boost on Friday by Yellen's comments and solid U.S. data.
Safe-haven gold edged up as buyers began to resurface after a 6 percent fall over the last few weeks.
"Markets are reacting to the possibility that the Fed might join the Bank of Japan in conducting policy to steepen the yield curve," Ric Spooner, chief market analyst at CMC Markets in Sydney, wrote in a note.
"In the Fed's case, this might amount to running the gauntlet of higher inflation with a very slow pace of monetary tightening."
Editing by Nick Zieminski and Bernadette Baum