After opening with modest gains, the Dow Jones Industrial Average managed to eke out a 1.74 point (0.01 percent) gain at 12,381.72 in closing trade.
The tech-rich Nasdaq Composite fell 8.91 points (0.32 percent) to 2,771.51, while the S&P 500-stock index, a broad measure of the markets, dropped 3.71 points (0.28 percent) to 1,324.46.
Stocks drifted as investors appeared to take a wait-and-see attitude to the start of the first-quarter earnings season.
"Market watchers will be looking closely to see if trading volume increases with the arrival of earnings season in order to assess investor sentiment and willingness to put cash to work," Briefing.com analysts said in a client note.
Dow component Alcoa was to kick off the reporting season after the market closes. Shares in the aluminum giant ended the day 1.1 percent lower at $17.72.