Mr Batten became the party’s latest acting leader after Henry Bolton was ousted following a vote of no confidence on Saturday.
Since being made interim leader, Mr Batten, who is a Ukip MEP for London, has been challenged on comments he made in the wake of the 2017 Westminster terror attack.
In a blog post, he branded Islam a “death cult” and said the attack in which a lone terrorist killed five people and injured 49 more was “just the latest in a long line of atrocities committed internationally” in the religion’s name.
Speaking to LBC’s Ian Collins, Mr Batten defended his comments and insisted he was right.
He said: “What people think and what people are prepared to say are two different things. I haven’t changed my mind on this.
“It’s always been founded on violence and oppression and intimidation. It was spread by invasion in its first 150 years and it’s carried on.
“If you look at the world, where you have Islamic people, they actually kill each other more than they killed non-followers of their religion.”
He also dismissed comments from a caller who argued now the Brexit referendum is over, Ukip is EDL-lite, anti-Muslim and anti-foreigner.
Mr Batten hit back: “This is such an uninformed, unintelligent response. I don’t really know what to say.
“We have got plenty of people of different origins in Ukip, people who actually were migrants themselves, because it is all about independence.”
In a separate interview on Sky News, Mr Batten defended his blog post as “factually and historically true”.
Speaking on the Sunday With Niall Paterson show, he said: “Anybody that cares to look at the history of Islam over the past 1,400 years will see that that is true.
“It glorifies death. They believe in propagating their religion by killing other people and martyring themselves and going and getting their 72 virgins.
“Not all of them – that’s not saying that all of them do believe that or do that – I’m saying that a significant minority believe that and they are the problem.
“But the trouble is they are justified in those beliefs by a literalist interpretation of their own so-called holy texts.”
Ahead of the Saturday’s no confidence vote, Mr Batten warned Ukip would be “finished” if Mr Bolton continued to serve as leader.
The former police officer had faced growing pressure to step down after it emerged his girlfriend Jo Marney had made racist comments about royal bride-to-be Meghan Markle.
He initially said he had split up with the 25-year-old model but later admitted he still had “strong affections” for her.