Department stores Macy's and Kohl's both jumped more than three percent, while Target rose 1.2 percent on indications that the early strength in the holiday shopping season persisted through Christmas.

But Apple dropped 2.8 percent, with analysts pointing to a report in Taiwan's Economic Daily of weak demand for the iPhone X. Apple suppliers such as Broadcom and Skyworks Solutions also fell.

About 15 minutes into trading, the Dow Jones Industrial Average was up slightly at 24,757.10.

The broad-based S&P 500 dipped 0.1 percent to 2,680.57, while the tech-rich Nasdaq Composite Index fell 0.6 percent to 6,921.04.

Analysts were anticipating a quiet period of trading after markets were closed Monday. Several international bourses were also closed on Tuesday for "Boxing Day."

Key data releases this week include the Conference Board's report on consumer confidence for December.

Home prices in the 20 biggest cities rose 0.2 percent in October from the prior month, according to the S&P Case-Shiller index.