SUNRISE: Donald Trump accused President Barack Obama on Wednesday of founding the militant Islamic State (IS) group that is wreaking havoc from the Middle East to European cities. A moment later, on another topic, he referred to the president by his 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 more times for emphasis.

The Republican presidential nominee in the past has accused his opponent, Democrat Hillary Clinton, of founding the militant group.

As he shifted the blame to Obama on Wednesday, he said “crooked Hillary Clinton” was actually the group's co-founder.

Trump has long blamed Obama and his former secretary of state — Clinton — for pursuing Mideast policies that created a power vacuum in Iraq that was exploited by IS, another acronym for the group.

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

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

IS began as Iraq's local affiliate of Al Qaeda, the group that attacked the US on September 11, 2001. The group carried out massive attacks against Iraq's Shia Muslim majority, fueling 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 airstrike but is still seen as the IS founder.

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

In June, when a shooter who claimed allegiance to IS killed 49 people in an Orlando, Florida, nightclub, Trump seemed to suggest Obama was sympathetic to the group when he said Obama “doesn't get it, or he gets it better than anybody understands”.

In the past, Trump has also falsely suggested Obama is a Muslim or was born in Kenya, where Obama's father was from. The president, a Christian, was born in Hawaii.

Trump lobbed the allegation midway through his rally at a sports arena, where riled-up supporters shouted obscenities about Clinton and joined in unison to shout “lock her up”.

He railed against the fact that the Orlando shooter's father, Seddique Mateen, was spotted in the crowd behind Clinton during a Monday rally in Florida, adding, "Of course he likes Hillary Clinton".

Sitting behind Trump at his rally on Wednesday was former Republican Mark Foley, who resigned in 2006 after allegations he sent sexually suggestive messages to former House pages.