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.

OPINION: Immigrants and Donald Trump - It's a complicated story

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.

READ MORE: US election 2016 - Third parties are voiceless

In June, when a gunman who claimed allegiance to ISIL killed 49 people in a 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 that Obama is a Muslim or was born in Kenya, where Obama's father was from.

Trump lobbed the allegation halfway through his rally at a sports arena, where riled-up supporters shouted obscenities about Clinton and shouted "lock her up”.

He also 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, saying: "Of course he likes Hillary Clinton."

Trump has been criticised over the past week for comments he made suggesting gun rights advocates could stop Clinton from becoming president and picking new, anti-gun Supreme Court judges, by using their second amendment rights, which allow them to bear arms.

"Hillary wants to essentially abolish the Second Amendment," Trump told a rally in North Carolina.

"If she gets to pick her judges, nothing you can do folks," Trump said. "Although the Second Amendment people - maybe there is, I don't know."

Trump's campaign spokesman later denied allegations that the comments were advocating for Clinton to be assassinated.