Even as the fallout from Target's holiday security breach continues -- the retailer's chief information officer resigned last week -- the brand is slowly returning to a normal marketing cadence.

Shoppers visiting its stores are being prompted to sign up for the retailer's credit card. Social-media channels have been turned over to product and partner news. And an campaign promoting the idea of the "Target Run" will roll out TV ads March 30.

"As we got through the holidays, we took a step back and said 'What are the things on the docket for 2014 that will support the business?'" said Jeff Jones, Target's CMO, who is responsible for investor relations, crisis communications, public relations and marketing communications. "Because the investigation is ongoing, it requires us every week -- if not more regularly -- to make sure we're very deliberate about all the things we're doing."

While the breach has influenced every facet of Target's business, including marketing, the retailer hasn't shied away from advertising intended to drive traffic to its stores. Mr. Jones said the breach, which was disclosed Dec. 19 and cost the retailer $17 million in the fourth quarter, has not had a material impact on its marketing budget. Last year, Target spent $631 million on measured media through November, according to Kantar Media.

The concept for the "Target Run" campaign, which will promote everything from tissues to ice cream, is the quick trip to Target that shoppers make for essentials. One ad features the copy, "Make an I-didn't-know-I-had-muscles-there run," along with images of Icy Hot, Advil and a bag of frozen peas. Another ad says, "Make a but-it's-the-tourney run," and shows Coors Light, cheese puffs and a basketball. The campaign, led by agency Mono, will run through January 2015.

Target did, however, shelve a campaign slated to break during the Olympics. That campaign, themed "Around for Good," highlights the retailer's efforts to be a good corporate citizen, from its community-service efforts to its sustainably sourced seafood.

Mr. Jones said the retailer postponed that campaign after deciding it felt "tone deaf" in light of the security breach. The campaign is expected to launch later this year, though a date has not been determined. Likewise, Target temporarily stopped prompting shoppers to apply for its store credit card in the wake of the breach. In mid-January those prompts resumed.

The retailer continues to carefully monitor consumer sentiment, including measures around favorability, integrity and trust, Mr. Jones said. While those measures have all rebounded in the short-term when Target has made statements related to the breach -- CEO Gregg Steinhafel's apology and the chain's commitment to speed up a $100 million program to implement the use of chip-enabled smart cards to protect against cyber theft -- they have not yet recovered.

Those gauges will be carefully watched throughout this year, especially as the holidays approach. Though the breach will eventually cease to be top-of-mind for consumers, it's a given that media reports will drag it back into consumers' consciousness as the holiday season approaches. "We're in the early days of planning for that," Mr. Jones said.