U.S. Republican presidential front-runner Donald Trump is now blaming both President Barack Obama and Democratic presidential hopeful Hillary Clinton for the creation and rise of the Islamic State (ISIS).

He is also claiming that he has predicted the burning of the Saudi Embassy in Tehran on Saturday as part of the conflict between Saudi Arabia and Iran.

In a rally in Biloxi, Mississippi, on Saturday night, Trump said Obama and Clinton "created ISIS," calling them a "bunch of dishonest people," Business Insider reported.

Trump followed this up with a new accusation against Clinton on Sunday, saying her decisions when she was Secretary of State in Obama's first term led to unnecessary deaths on both sides in the Middle East.

"She has caused tremendous death with incompetent decisions," Trump told CBS' "Face the Nation" on Sunday. "She caused a lot of the problems that we have right now. You could say she caused the migration," he said as reported by USA Today.

"The entire world has been upset. The entire world, it's a different place. During Barack Obama and Hillary Clinton's term, she's done a horrible job."

Trump said getting rid of Saddam Hussein in Iraq—a policy of Obama's predecessor, George W. Bush—has led to the rise of the ISIS. "All of this has led to tremendous death and destruction," he said. "And she, for the most part, was in charge of it, along with Obama."

Trump and Clinton have been at loggerheads in recent weeks after Clinton said that his provocative campaign-trail statements had become propaganda for the ISIS, especially his proposal to bar Muslims from entering the U.S.

Trump demanded that Clinton apologise, but her campaign replied at the time, "Hell no. Hillary Clinton will not be apologising to Donald Trump for correctly pointing out how his hateful rhetoric only helps ISIS recruit more terrorists."

Days later, a video purportedly produced by the Somali terrorist group al-Shabaab came out with the voice of Trump calling for the "total and complete shutdown" of Muslims entering the U.S.

In reaction, Michael Cohen, a top Trump aide, tweeted on Saturday suggesting that Clinton was behind the new terrorist recruiting video featuring Trump, CNN reported.

Later on Sunday morning on "Face the Nation," Trump responded to his "starring role" in a recent terrorist recruitment video, according to CBS News.

After programme host John Dickerson played a portion of the al-Shabab video, Trump said he shouldn't be blamed for this.

"I bring it up. Other people have called me and say, 'You have guts to bring it up because frankly, it's true but nobody wants to get involved. Now people are getting involved."

Dickerson then asked, "Does it concern you at all that you're being used in essentially a recruitment video by a terrorist organisation?"

"They use other people, too," Trump said. "What am I going to do? I have to say what I have to say. And you [know] what I have to say? There's a problem. We have to find out what is a problem. And we have to solve that problem."

Earlier in Mississippi, Trump commented on the execution in Saudi Arabia of a prominent Shiite cleric that triggered massive protests in Iran. "I see a lot of things happening," he said.

"One thing I see out there just happened today in Tehran," he said. "They're burning down the Saudi Embassy, you see that? Now, what that is, is Iran wants to take over Saudi Arabia. They always have. They want the oil, OK? They've always wanted that."

In Saturday's rally, Trump also blasted Clinton, saying she "shouldn't be allowed to run" because of the private email system she used for her State Department work.

"She should be in jail, by the way, for what she did," Trump said. "Everybody knows she should be in jail. What she did with the emails is a disgrace," he said.

Earlier on Friday, five planes flew over the annual Rose Parade in Pasadena, California, writing messages in the sky that included "America is great! Trump is disgusting. Anybody but Trump, US."

CBS News said an Alabama businessman, Stan Pate, was behind the airborne protest targeting Trump.