* ISM services index expands more than expected
* Bank of Japan to pump more funds into economy
* Indexes up: Dow 1.2 pct, S&P 1.5 pct, Nasdaq 1.7 pct (Updates with ISM data, quote)
By Ryan Vlastelica
NEW YORK, Oct 5 (Reuters) - U.S. stocks rose more than 1 percent in a broad rally on Tuesday after encouraging U.S. services sector data and new steps by central banks to fight economic weakness abroad reassured investors.
The pace of growth in the U.S. manufacturing sector accelerated more than forecast last month, while hiring also picked up, according to an industry report.
"This confirms that we're continuing to see the economy grow, though at a slow pace," said Kate Warne, investment strategist at Edward Jones in St. Louis. "I suspect we'll keep seeing expansion in the month ahead."
The Bank of Japan will pump more funds into the struggling economy and keep rates close to zero, while Australia's central bank also kept rates low. The Nikkei closed up 1.5 percent on the fresh dose of stimulus, while global shares rose 1.5 percent.
"It's hard to argue that we'd be better off without these quantitative easing programs, and it increases the case for Bernanke to move ahead with something similar here," said Wayne Kaufman, chief market analyst at John Thomas Financial in New York.
The Dow Jones industrial average was up 129.99 points, or 1.21 percent, at 10,881.26. The Standard & Poor's 500 Index was up 16.76 points, or 1.47 percent, at 1,153.79. The Nasdaq Composite Index was up 40.50 points, or 1.73 percent, at 2,385.02.
U.S. Federal Reserve Chairman Ben Bernanke said Monday the Fed's asset purchases lowered borrowing costs and helped the economy, adding that that more buying could further ease conditions.
Among active stocks, Walgreen Co gained 4 percent to $34.43 after the drugstore chain posted September same-store sales that rose more than expected.
Chevron Corp rose 1.5 percent to $82.52 a day after the Dow component said it plans to resume quarterly stock buybacks of up to $1 billion.
With the dollar index falling to its weakest since January, commodity prices rose. Crude oil jumped 1.1 percent and neared its highest price since Aug. 6, while gold hit a record high above $1,333 an ounce.