The Dow rose 111.42 points, or 0.7 percent, to 15,680.35. The Dow also got a big boost from IBM, which announced that it would but $15 billion more of its own stock.
The Fed is in the middle of a two-day policy meeting at which it's expected to maintain its $85 billion worth of bond purchases every month. That program is aimed at stimulating economic growth by keeping borrowing rates very low. The Fed will announce its decision Wednesday afternoon.
"The expectation that the Fed remains clearly on hold is the catalyst for this march higher," said Quincy Krosby, a market strategist at Prudential Financial.
IBM rose $4.77, or 2.7 percent, to $181.12, accounting for about a quarter of the Dow's gain.
The Standard and Poor's 500 index rose 9.84 points, or 0.6 percent, to 1,771.95, its seventh record high this month.
About half the companies in the S&P 500 have reported earnings for the third quarter. So far, most are doing better than investors expected. Companies in the index are forecast to log third-quarter earnings growth of 4.5 percent, according to data from S&P Capital IQ.
The Nasdaq composite rose 12.21 points, or 0.3 percent, to 3,952.34.
The Nasdaq Stock Market was hit with another glitch. Nasdaq indexes weren't updated from 11:53 a.m. to 12:37 p.m. because of a technical problem that was caused by human error, the exchange operator said in a statement. Trading of Nasdaq-listed stocks wasn't affected.
On Sept. 4, the Nasdaq had a brief outage in one of its quote dissemination channels, but trading wasn't disrupted. On Aug. 22 the exchange suffered a three-hour trading outage that was also attributed to problems with the exchange's price disseminating system.
Two economic reports came in relatively weak, which may have encouraged some investors by suggesting that any slowdown in the Fed's stimulus could be a ways off.
Retail sales fell 0.1 percent in September, the weakest showing since March, as auto sales dipped. Americans' confidence in the economy fell this month to the lowest level since April. People were worried about the impact of the 16-day partial shutdown of the U.S. government.
"The data that has been the most attractive to (stock) markets seems to be the data that maintains the status quo," said Brad Sorensen, the director of market and sector analysis at the Schwab Center for Financial Research.
The yield on the 10-year Treasury note fell to 2.50 percent from 2.52 percent Monday.
In commodities trading, oil fell 48 cents, or 0.5 percent, to $98.20 a barrel. Gold dropped $6.70, or 0.5 percent, to $1,345.50 an ounce.