Jack Dorsey denied the videos were kept on the social media platform because of the publicity the US president generates.
Twitter has claimed its decision not to remove violent far-right videos shared by Donald Trump had nothing to do with the episode making global headlines.
A row erupted between Theresa May and the US president when he retweeted three anti-Muslim videos posted by the deputy leader of fringe political group Britain First.
Two featured violent scenes, including someone being pushed off a roof and another person being assaulted, leading Twitter users to suggest they breached the site’s guidelines.
A previous statement from Twitter indicated the content was allowed to remain online as it stoked debate.
It pointed to guidance in its help centre which said: “There may be the rare occasion when we allow controversial content or behaviour which may otherwise violate our rules to remain on our service because we believe there is a legitimate public interest in its availability.”
On Friday, Twitter co-founder Jack Dorsey rowed back on the suggestion, saying: “We mistakenly pointed to the wrong reason we didn’t take action on the videos from earlier this week.”
In a series of posts shared from the Twitter Safety account, the social media giant appeared to set out why Mr Trump’s tweets remained on the site.
It wrote: “Earlier this week Tweets were sent that contained graphic and violent videos. We pointed people to our Help Center to explain why they remained up, and this caused some confusion.
“To clarify: these videos are not being kept up because they are newsworthy or for public interest. Rather, these videos are permitted on Twitter based on our current media policy.
“We will continue to re-evaluate and examine our policies as the world around us evolves. We appreciate the feedback and will continue to listen.”
One user replied to Mr Dorsey’s post, asking him if he thought the reason the posts stayed up was due to Twitter needing Mr Trump to drive traffic to the website, to which the tech chief replied: “No, I don’t.”
According to Twitter’s media policy, a post breaches guidelines if it contains “gory media related to death, serious injury, violence or surgical procedures”.
It lists examples including the moment someone dies, a gruesome crime scene or bodily harm, torture, dismemberment or mutilation.
The Prime Minister previously said Mr Trump was “wrong” to retweet videos posted by Britain First’s deputy leader Jayda Fransen, which she condemned as a “hateful organisation” dedicated to spreading division and mistrust.
The extraordinary flare-up between the two key allies came after Mr Trump responded directly to her assertion â originally made through her official spokesman â that his re-postings had been wrong.
In a trademark tweet, he wrote: “@Theresa_May, don’t focus on me, focus on the destructive Radical Islamic Terrorism that is taking place within the United Kingdom. We are doing just fine!”
Mrs May has since rejected calls to cancel his controversial state visit, despite an outcry from MPs, insisting she remained committed to the “special relationship” between the UK and US.
Britain First leader Paul Golding boasted the group had gained hundreds of new membership applications and its Facebook posts were reaching hundreds of thousands more users.
Fransen, 31, from Penge, south-east London, is on bail facing trial over four charges of causing religiously aggravated harassment as part of a Kent Police investigation into the distribution of leaflets and the posting of online videos during a trial held at Canterbury Crown Court in May.
She will go on trial at Folkestone Magistrates’ Court on January 29, alongside Golding, who faces three similar charges.
Fransen will also appear in court in Northern Ireland in December charged with using threatening and abusive language in connection with a speech she made at an anti-terrorism demonstration in Belfast on August 6.
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