It follows a similar apology by retailer Paperchase last month.
On Saturday, Pizza Hut urged its followers on Facebook to pick up a copy of The Sun on Sunday to find out how get a free pizza.
Several on Twitter then said that they would boycott the restaurant chain until it stopped advertising in The Sun. In response, Pizza Hut Delivery tweeted to say: "We apologise for any offence caused as a result of this partnership. The aim of this offer was simply to give our customers the chance to enjoy a free pizza to share with their family and friends."
We apologise for any offence caused as a result of this partnership. The aim of this offer was simply to give our customers the chance to enjoy a free pizza to share with their family and friends.— Pizza Hut DeliveryUK (@pizzahutdeliver) December 2, 2017
The campaign group Stop Funding Hate, which targets businesses that advertise in The Sun, Express, and Daily Mail, then mentioned Pizza Hut on Twitter, suggesting that The Sun has been accused of fuelling prejudice.
A spokesman for the group told PRWeek: "With growing concern that the hate in our media is fuelling hate crime on our streets, is it any wonder so many of us don't want to subsidise this through our shopping. We'd urge the Sun to reflect on why so many feel attacked by its hostile coverage, and why brands might want to distance themselves."
The Pizza Hut UK account also tweeted a similar message to individuals.
We apologise for any offence caused as a result of this @pizzahutdeliver promotion. The aim of the offer was simply to give customers the chance to enjoy a free pizza to share with their family and friends— Pizza Hut UK (@pizzahutuk) December 3, 2017
A spokesman for the Sun said: "The Pizza Hut promotion is continuing as planned until Thursday so readers will no doubt be enjoying their margheritas in their thousands."
Stop Funding Hate has also played a role in encouraging The Body Shop, Lego, Evans Cycles and Joy to pull advertising in various papers, while just last month, stationery and gift retailer Paperchase also apologised to its followers on social media for a promotion it ran in the Daily Mail. The retailer said: "We apologise if we have let you down on this one. Lesson learnt."