The claim, which Democratic candidate Hillary Clinton said "amazed" her, came in the third and last presidential debate just 20 days before Americans head to the polls. During their fractious, occasionally raucous face-off in Las Vegas, Nevada, the candidates also touched on abortion, immigration, national debt and foreign policy.
The fight for Mosul, which began Sunday, is being led by a diverse 94,000-member coalition comprised of Iraqi security forces, Kurdish Peshmerga allies and thousands of irregulars from various Iraqi minority groups after more than two years of ISIS rule.
The US is advising on the effort to reclaim Iraq's second-largest city and ISIS's top stronghold in the country. The battle is expected to take months, officials say, but would be a crucial step in routing the terror group.
'She wanted to look good... so they're going in'
On Wednesday evening, Trump insinuated that Iraq launched the mission to help Clinton win the White House.
"The only reason they did it is because she's running for the office of president and they want to look tough," Trump said. "They want to look good."
"She wanted to look good for the election," he continued, "so they're going in."
Clinton said Trump's claim reflected his belief in conspiracy theories.
"I'm just amazed that he seems to think that the Iraqi government and our allies and everybody else launched the attack on Mosul to help me in this election, but that's how Donald thinks," Clinton said. "You know, he always is looking for some conspiracy."
The exchange was part of a contentious back-and-forth between the candidates over the war in Iraq, the war in Syria and the rise of ISIS, for which the New York real-estate mogul blamed Clinton.
"We should never have let ISIS happen in the first place," Trump said.
Clash over Aleppo
Moderator Chris Wallace of Fox News asked the candidates about the ongoing siege of Aleppo in Syrian. The regime of President Bashar al-Assad, along with its Russian allies, are bombing the rebel stronghold where an estimated 400,000 people -- 100,000 of them children -- are trapped.
"They're being slaughtered because of bad decisions," Trump said.
When Wallace asked Trump about Russian responsibility for large-scale deaths in bombings there, the Republican candidate didn't respond, saying instead that "Aleppo is a disaster," and adding that "a lot of this has happened because of Hillary Clinton."
Later, discussing Syria, Trump predicted greater upheaval in future and turned to Clinton, saying "wait 'til you see what happens in the coming years," and blaming her. "Thanks a lot, Hillary," he said.
Clinton made a clear pledge to pursue a no-fly zone in Syria if elected -- a policy decision President Barack Obama has declined to take. Critics of the idea say that, among other problems, it would expose US jets to the danger of accidental clashes with Russian planes.
Clinton said she was "well aware of the concerns" about establishing these zones that Obama and some military officials have expressed. But she said, "I think a no-fly zone could save lives and hasten the end of the conflict."
"This would not be done on the first day," she said, adding that her administration would make clear to the Russians and Syrians that the purpose would be to create a safe area for ordinary Syrians fleeing the violence.
"I think we could strike a deal and make it very clear to the Russians and the Syrians this would be in the best interests of the Syrians," Clinton said.