The Dow Jones industrial average edged close to the 11,000 mark but failed to cross it for a second day.
The Dow ended down about 4 points, while broader indexes rose. Interest rates fell after rising on Monday.
For a second day, the Dow rose to within about a dozen points of the psychological milestone of 11,000 before retreating. It hasn't been above that mark in 18 months.
Shares of regional banks Regions Financial Corp. and SunTrust Banks Inc. rose following upbeat comments from analysts. Tech stocks were mixed after business software company CA Inc. said earnings for the year will come in at the lower end of its forecast. CA also said it would cut 1,000 jobs, or about 8 percent of its work force.
Massey Energy Co. fell more than 11 percent after an underground explosion Monday afternoon blamed on methane gas killed 25 coal miners about 30 miles south of Charleston, W.Va. Four others were missing Tuesday following the explosion about 1.5 miles from the entrance to Massey's Upper Big Branch mine. It was the worst U.S. mining disaster since 1984.
The stock market rose to its best levels of the day in afternoon trading when the release of minutes from the Federal Reserve's last meeting signaled that policymakers are more upbeat about the economy. Analysts said, however, that the minutes contained few surprises.
The quiet trading came as investors looked for clues about whether the market could continue its upward march. Stocks have been rising for 13 months but have made steadier advances since February following reports that signal the economy is improving. The Dow has risen for each of the past five weeks, its longest winning streak since mid-April last year.
"It's no longer a question of 'Is the recovery under way?' It's a question of the pace of the recovery," said Paul Ballew, chief economist at Nationwide Insurance in Columbus, Ohio.
Companies will begin reporting earnings for the January-March quarter next week so traders will have a better sense of whether the recent climb in stocks is justified.
The Dow fell 3.56, or less than 0.1 percent, to 10,969.99. It was only the Dow's sixth drop in the past 27 trading days.
The Standard & Poor's 500 index rose 2.00, or 0.2 percent, to 1,189.44. The index is at an 18-month high.
The Nasdaq composite index rose 7.28, or 0.3 percent, to 2,436.81. The index stands at its best level since August 2008.
Bond prices rose, pushing yields lower. The yield on the benchmark 10-year Treasury note fell to 3.96 percent from 3.99 percent late Monday.
The 10-year yield climbed above 4 percent during trading Monday for the first time since June. It is approaching levels not seen since October 2008.
A rise in rates signals in part that investors feel more comfortable about the recovery. That is hurting demand for safer holdings like Treasurys. However, a jump in borrowing costs could slow the rebound by driving up borrowing costs.
The dollar rose against other major currencies. Gold rose.
Crude oil rose 22 cents to $86.84 per barrel on the New York Mercantile Exchange after reaching an 18-month high of $87.09 a barrel.
Whether the recovery can continue depends on the labor market. On Friday, the government reported that the economy posted its biggest job gain in three years in March.
"You have to have the average consumer making more this year than last year in order for the economy to grow longer-term," said Jason D. Pride, director of investment strategy at Glenmede in Philadelphia.
Regions Financial rose 36 cents, or 4.4 percent, to $8.55 after Credit Suisse raised its price target on the bank. Shares of SunTrust rose after Credit Suisse said foreign banks could see SunTrust as an attractive takeover target. The stock advanced 97 cents, or 3.5 percent, to $28.71.
CA shares fell 45 cents, or 1.9 percent, to $23.40.
Massey fell $6.24, or 11.4 percent, to $48.45.
Three socks rose for every two fell on the New York Stock Exchange, where volume came to a light 936.2 million shares compared with 902.4 million Monday. The lighter trading volume means that fewer investors are trading in the market. That allows fewer buyers to drive stocks higher.
The Russell 2000 index of smaller companies rose 3.83, or 0.6 percent, to 701.48. The Russell reached a 12-month high of 702.65 during trading.
Britain's FTSE 100 rose 0.6 percent, Germany's DAX index rose 0.3 percent, and France's CAC-40 rose 0.5 percent. Japan's Nikkei stock average fell 0.5 percent.