Defending his previous claim that Islam is a "death cult", Gerard Batten said in an interview with Sky News that his comments were "factually and historically true".
Mr Batten stepped in as interim leader after party members voted to oust Henry Bolton.
Mr Bolton, who was only elected in September 2017, was sacked after party members voted by 867 to 500 to express their lack of faith in his ability to lead the party after the scandal over his lover.
London MEP Batten has promised to make Ukip a populist force and win back donors for the cash-strapped party.
He was also confronted in his Sky News interview about suggesting compulsory declaration of loyalty from Muslims.
Mr Batten said: "[Islam] glorifies death - they believe in propagating their religion by martyring themselves.
"A significant minority believe that, and they are the problem."
He added: "I don't think it's unreasonable to say that people who come and live in our country should reject those dark age ideologies which some of them bring with them."
Ukip will face a fresh leadership election within 90 days after Mr Bolton lost the no confidence motion.
Mr Batten issued a dismissive response to suggestions Mr Bolton could take legal action.
Asked what his message to Mr Bolton was he said: "Get on with the rest of your life."
Mr Batten, who did not rule out standing for the leadership on a permanent basis, said: "I feel optimistic that Ukip can and will grow stronger and more successful because ordinary patriotic people want, need and deserve a party that represents their interests.
"Ukip came into being because it filled a political vacuum. That vacuum still exists. I want Ukip to be a 'populist' party - popular because its policies are what people actually want."
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