Donald Trump today called President Barack Obama and Democratic candidate Hillary Clinton "co-founders" of Islamic State, igniting fresh criticism of his inflammatory campaign style.

The Republican presidential candidate has previously attacked Obama and Clinton, who was Secretary of State from 2009-13, for the way in which the US withdrew from Iraq after the war, saying it left a power vacuum which helped create the militant Islamist group that has seized parts of Iraq and Syria.

But at a campaign rally in Florida on Wednesday night, Trump first made the assertion that Obama was the "founder" of ISIS, and repeated the claim about the President and Clinton in an interview on Thursday morning with CNBC.

"He [Obama] was the founder of ISIS. And so was she. I mean I call them co-founders," said Trump, who claims to have opposed the Iraq war. "He shouldn't have gotten out way he got out. It was a disaster, what he did," he told CNBC.

Obama opposed the 2003 invasion of Iraq and campaigned for the White House in 2008 on a promise to end the war. The US pulled out combat troops in 2011. In 2014, ISIS declared an Islamic caliphate in Syria and Iraq.

Reacting to the comments, a spokesperson for Clinton, Jesse Lehrich pointed to US advances against the militant group in Libya this week. "FYI – US-backed militias retook ISIS's stronghold in Libya today thanks to Obama-authorised air strikes," he said in a tweet on Wednesday night.

Trump refused to back down, asking on CNBC: "Is there something wrong with saying that? Why...are people complaining that I said he [Obama] was the founder of ISIS? All I do is tell the truth, I'm a truth teller."

Trump drew criticisms from his own party. Senior Republican Sean Duffy said Obama and Clinton did not found Islamic State and urged Trump to stay on message.

"Stay on script. Don't go off script. Read your teleprompter and you're going to be fine," Duffy said on MSNBC.

Trump denied that he had made many mistakes. "I don't think I've made too many errors," he told CNBC. The businessman added that if he loses he can return to a comfortable life.

"It's not what I'm looking to do - I think we're going to have a victory but we'll see," Trump added.

Additional reporting by Reuters.