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Donald Trump accused President Barack Obama on Wednesday of founding the Islamic State of Iraq and the Levant group (ISIL, also known as ISIS) that is wreaking havoc from the Middle East to European cities.

A moment later, on another topic, he emphasised the president's full legal name: Barack Hussein Obama.

"In many respects, you know, they honour President Obama," Trump said during a raucous campaign rally outside Fort Lauderdale, Florida. "He is the founder of ISIS."

He repeated the allegation three times.

"He's the founder of ISIS, okay?" he added. "He's the founder. He founded ISIS."

Trump has long blamed Obama and his former Secretary of State Hillary Clinton for pursuing Middle East policies that created a power vacuum in Iraq that was exploited by ISIL.

He has sharply criticised Obama for announcing that he would pull US troops out of Iraq, a decision that many Obama critics say created the kind of instability in which groups such as ISIL thrive.

The White House declined to comment on Trump's accusation.

The former property mogul and reality TV star went on to criticise Clinton, his Democratic party rival for the presidency.

"And I would say, the co-founder would be crooked Hillary Clinton," he said.

The Republican presidential nominee has in the past accused Clinton of "founding" the group.

Assassination allegations

ISIL began as Iraq's local affiliate of al-Qaeda and has carried out massive attacks against Iraq's Shia Muslim majority, fuelling tensions with al-Qaeda's central leadership.

The local group's then-leader, Jordanian-born Abu Musab al-Zarqawi, was killed in 2006 in a US air strike but is still seen as its founder.

Trump's accusation - and his pointed use of the president's middle name, Hussein - echoed previous instances where he has questioned Obama's loyalties.