It's unclear what caused the outages, though the system has since been restored.
A Target spokesperson says there is no evidence of a security breach or failure.
Target said the issue was resolved by Sunday evening and that it wasn't related to security.
"Our teams are troubleshooting now and we apologise for the inconvenience, " the retailer tweeted http://bit.ly/2WKO1HY, adding that it would provide an update soon. "We never want to disappoint any guests and we're working tirelessly to ensure these issues don't happen again".
In Blaine, Minn., one Twitter user posted a video of customers waiting in line, writing, "Registers are down.#targetfail".
A defect in a network device in June 2014 also caused problems with Target's payment processing systems, according to media reports.
Ex-Iranian Diplomat Claims Israel Behind Oil Tanker Attacks
"While he was there [it] replied to his efforts by attacking two tankers, one of which was Japanese". Iran has denied involvement, accusing the US of "Iranophobia" and trying to "sabotage diplomacy ".
"We appreciate all of our store team members who worked quickly to assist guests and thank everyone involved for their patience", Target officials wrote in a statement.
Earlier on Saturday, Target tweeted that it was aware guests could not make purchases and apologized for the inconvenience.
But some shoppers posting on their Twitter accounts Saturday painted a different picture as they vented about excruciatingly long lines but expressed sympathy for the Target employees trying to cope with the situation.
Target faced massive technical difficulties on Saturday, as customers across the U.S. found themselves unable to check out at the retailer.
The Minneapolis company said customers caught in up the checkout slowdown have no reason to worry. The store says it was not a data breach and no customer information was compromised.