He also called Democratic nominee Hillary Clinton a “co-founder”, igniting fresh criticism of his inflammatory campaign style.
Asked in an interview with CNBC whether it was appropriate for him to call the sitting president of the US the founder of a terrorist organisation that wants to kill Americans, Mr Trump reaffirmed his accusation.
“He was the founder of Isis, absolutely,” said Mr Trump. He blamed the president for his decision to withdraw troops, which some argue created a power vacuum in which extremist groups like IS thrive.
Mr Trump said the US “should have never gotten in” the war, but also should not “have got out the way he got out”.
Mr Trump now claims that he was opposed to the Iraq War from the beginning, despite evidence to the contrary.
His remarks followed a troubled week for the Republican candidate. Party leaders urged Mr Trump to focus on the campaign to beat Ms Clinton after he drew strong criticism for a persistent confrontation with the family of Muslim American soldier who died in Iraq and for his initial refusal to support prominent Republican congressional candidates in their primary races.
Recent opinion polls have shown Mr Trump losing ground to Ms Clinton, a former US senator and first lady, in the November 8 election. An average of polls by RealClearPolitics has Clinton 7.7 percentage points ahead, at 48% to his 40.3%.
“He [Obama] was the founder of Isis. And so was she. I mean I call them co-founders,” said Mr Trump. “He shouldn’t have gotten out way he got out. It was a disaster, what he did.”
Mr Obama had opposed the Iraq war and campaigned for the White House in 2008 on a promise to end it. The US pulled out combat troops in 2011.
Islamic State in Iraq and Syria, also known as Isis or Isil, had its roots in the al-Qaida insurgency that arose after the US led an invasion of Iraq in 2003. Known for its brutality, the group in 2014 declared an Islamic caliphate in Syria and Iraq, where fighting continues to rage.
Clinton spokesman Jesse Lehrich, in response to Mr Trump’s comments, pointed to US advances against the militant group in Libya this week.
“US-backed militias retook Isis’s stronghold in Libya today thanks to Obama-authorised air strikes,” he said.
Mr Trump did not back down, asking on CNBC: “Is there something wrong with saying that? Why are people complaining that I said he was the founder of Isis? All I do is tell the truth, I’m a truth teller.”
Supporters of Trump, who has never held elected office, like his combative and often insulting style but it has drawn wide criticism, not just from the Clinton campaign. Many Republicans have urged him to change tactics and focus on the economy, while other senior figures have said they will not vote for him.
US representative Sean Duffy, a Republican from Wisconsin who backs Mr Trump, said Mr Obama and Mr Clinton did not found IS and urged Mr Trump to stay on message.
“Stay on script. Don’t go off script. Read your teleprompter and you’re going to be fine,” said Mr Duffy.
However, Mr Trump bristled at the notion he should change.
“I don’t think I’ve made too many errors,” he told CNBC. If his style costs him the election in 90 days, he goes back to a good life, he said.
“It’s not what I’m looking to do. I think we’re going to have a victory but we’ll see,” he said.
Meanwhile, a Glasgow-born photographer who watched his friend Robert Kennedy gunned down in the 1968 US presidential campaign fears Mr Trump’s rhetoric could lead to more politically motivated shootings.
Harry Benson, whose pictures of a dying Kennedy are among the most iconic of the last century, said Mr Trump may have put Democrat lives at risk.
Mr Trump said “second amendment people” could find a way to stop Ms Clinton introducing tougher gun laws, adding: “That will be a horrible day.”
Ms Clinton accused Mr Trump of a “casual inciting of violence” and warned “words can have tremendous consequences”.
Mr Benson, who has covered US presidential campaigns for more than 50 years, said he has never seen a campaign as “crazy” as this one.
A retrospective of his work, including his pictures of Robert and brother John who was assassinated in 1963, has gone on display at the Scottish parliament.
“I was friends with Bobby Kennedy and I followed him right through to his death,” he said.
“I’ve photographed Donald Trump for 40 years. I did 10 pages of photos of Trump for Time magazine last week. He hasn’t changed.
“I’ve never seen anything like it. I’ve never seen anything so crazy. There was a bit of decorum in the other elections but there is none in this.
“Trump saying ‘crooked Hillary’ has turned off a lot of the public. What he might have done is get other people shot, Clinton supporters or people with a Clinton badge.”
The retrospective includes photos of a young Clinton cosying up to husband Bill shortly before he received the Democrat nomination for president in 1992.
“I’ve followed Hillary over the years, and clever people who know what they are talking about say she is very competent,” he said.
Mr Benson also admitted a fondness for much- maligned president Richard Nixon and the most senior of his infamous ‘President’s Men’.
He photographed former attorney general John Mitchell celebrating after being acquitted of obstructing the Watergate investigation in 1974 and they discussed their shared fondness for Scottish vaudeville singer Harry Lauder.
Mr Benson also has a controversial choice for the person he would most like to photograph. “I would like to do Putin,” he said.