Hillary Clinton admonished rival Donald Trump on Thursday for claiming that she and Barack Obama were the founders of the Islamic State, saying anyone who would "sink so low" should never be president.

"No, Barack Obama is not the founder of ISIS," Clinton tweeted.

"Anyone willing to sink so low, so often should never be allowed to serve as our Commander-in-Chief."

Trump again roiled the presidential campaign late Wednesday, telling a rally in Florida that Obama "is the founder of ISIS."

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

Republicans have long stated that the foreign policies of Obama and his then-secretary of state Clinton share blame in helping create conditions that allowed IS to grow in Iraq and Syria.

IS was founded in 2013, months after Clinton left the State Department. It was born out of the terror group Al-Qaeda in Iraq that grew in strength in 2006 following Republican president George W. Bush's decision to invade Iraq in 2003.

The group flourished with Obama's withdrawal of US troops from Iraq in late 2011. Republicans said Obama was slow to recognize the threat when he said in 2014 that the Islamic State was a "JV" -- junior varsity -- team even though they gained ground in Syria and Iraq.

"It goes without saying that this is a false claim from a presidential candidate with an aversion to the truth and an unprecedented lack of knowledge," Clinton senior policy advisor Jake Sullivan said in a statement.

"This is another example of Donald Trump trash-talking the United States."

Sullivan warned that Trump was "echoing the talking points of (Russian President Vladimir) Putin and our adversaries to attack American leaders and American interests, while failing to offer any serious plans to confront terrorism or make this country more secure."

The Democratic National Committee weighed in, saying Trump "should apologize for his outrageous, unhinged and patently false suggestions."

But on Thursday, Trump doubled down, telling homebuilders in Miami Beach, Florida that Obama and Clinton were "the founders of ISIS."

"ISIS will hand her the most valuable player award," he said of Clinton, 68.

Earlier Thursday, Trump stood firm when asked by CNBC whether it was appropriate to say a sitting US president founded a jihadist group determined to kill Americans.

"Is there something wrong with saying that?" Trump, 70, said. "Are people complaining that I said he was the founder of ISIS?"

"All I do is tell the truth. I'm a truth-teller."

With his poll numbers slipping after two nightmarish weeks, the billionaire real estate mogul also sought to minimize the personal cost of a potential defeat against Clinton.

"If at the end of 90 days I fall short... even though I'm supposed to have a lot of good ideas, it's OK. I go back to a very good way of life," he told the network.

"It's either going to work or I'm going to, you know, I'm going to have a very, very nice long vacation."

Last week, Trump prepared his followers for possible defeat, warning a rally that the November 8 election will be "rigged."