"Our teams are solving the problems and we apologize for this inconvenience and we will provide an update as soon as possible," the company said in a separate tweet.
Social media users said the cash registers were not working properly in dozens of stores across the country and had posted images of long lines.
"That's how you stop America," said a Minnesota reporter on Twitter, accompanied by a photo of the error message posted on a cashier's booth. . "Every register at Richfield [Target] is off."
Employees from three different locations in Georgia told CNN that the logs were offline for about 45 minutes at 3 pm Eastern Time.
The systems issue came during a busy weekend for buyers before Father's Day Sunday.
It is unclear how many Target stores were affected or what caused the outage. The company's headquarters did not immediately respond to requests for details of the problem.
Target has 1,800 sites in the United States and a presence in India.