"No, Barack Obama is not the founder of ISIS," Clinton tweeted, using another name for the terrorist group. She further accused Trump of a "smear" against the president and stressed that he was not fit to serve as commander-in-chief of the United States.
Trump had told a crowd attending a rally in Miami that Obama was "the founder of ISIS" - a claim he later also repeated in the city of Kissimmee, also in Florida.
"And I would say, the co-founder would be crooked Hillary Clinton," Trump said at the Miami event, and later added that IS was "hoping" for Clinton - presumably to win the election.
The Democratic National Committee has called on the Republican candidate to "apologize for his outrageous, unhinged and patently false suggestions," to which the 70-year-old Trump replied that he had told the truth.
"This is another example of Donald Trump trash-talking the United States," Clinton's senior policy adviser, Jake Sullivan, said in a statement.
The White House declined to comment on Trump's statement.
A history lesson
Republican leaders have repeatedly stated that the foreign policies of President Obama and his former secretary of state, Clinton, were to blame for helping to create the conditions that allowed the IS group to grow in Iraq and Syria. However, the jihadi organization was officially founded in 2013, months after Clinton had left the State Department.
IS grew out of the extremist group al-Qaida in Iraq, flourishing in the power vacuum after the US troop withdrawal from Iraq in late 2011. American soldiers had been in Iraq for more than eight years following the US-led invasion of the country in 2003 under Republican President George W. Bush.
Trump has previously criticized Clinton for supporting the Iraq War in 2003 while she was a US senator. He also claimed that he opposed the war; however, in interviews he gave before the invasion he did express support for the invasion. He further has repeatedly criticized Clinton for her handling of a siege on the US diplomatic compound in Benghazi, Libya, in 2012.
Slumping support for Trump
Trump's remarks have landed the presidential hopeful in repeated controversy recently. Just days ago he had made comments that could amount to advocating gun violence - against Hillary Clinton. Trump caused alarm when he suggested that the "Second Amendment people" - referring to Americans who staunchly support gun rights - could act against Clinton.
Many Republicans even said that his Second Amendment remarks had crossed a line. Relatives of Republican President Ronald Reagan, who was shot and wounded in 1981, condemned Trump for his gun remarks. Family members of Democratic President John F. Kennedy, who was shot to death in 1963, expressed revulsion over Trump for voicing "the possibility of political assassination."
Donald Trump has been facing an uphill struggle to gain support for his campaign following two weeks of sliding poll numbers underscored by rejection by a series of fellow Republicans. A group of about 70 Republicans, including five former members of Congress, called on the Republican National Committee to stop supporting Trump in the wake of his recent remarks and instead focus on getting members of Congress re-elected.