The Dow Jones industrial average held on to a gain even though the overall stock market weakened.

A 2.6 percent rise in shares of Verizon Communications helped lift the Dow. The stock rose after a Financial Times blog said that Vodafone was considering a takeover bid for Verizon. Vodafone issued a statement saying that it had no such plans.

The Dow rose as high as 13,989 before retreating to close at 13,950.98, up 0.3 percent, another new record.

But broader market measures, including the Standard & Poor's 500 and the Nasdaq composite index, ended lower. 

"Market breadth today is not very good at all, so that would cause me a little bit of concern here for the very short-term," John Buckingham, chief portfolio manager at Al Frank Asset Management, told CNBC.

Weighing on investors minds have been the fallout from the collapse of the subprime mortgage market and high energy prices. They will be looking at a flurry of earnings reports this week, as well as data on inflation and the midyear testimony from the Federal Reserve chairman, Ben Bernanke.