"Certainly, in certain instances they are," Trump told Fox News host Bill O'Reilly when he asked whether the group has been "a fuse-lighter in the assassinations of these police officers."
"They certainly have ignited people and you see that ... It's a very, very serious situation and we just can't let it happen," Trump said.
Trump also called the group a "threat" and accused the group of "essentially calling death to the police," apparently referring to a 2014 video of protesters in New York City who chanted, "What do we want? Dead cops."
Those chants came during a protest organized by Millions March NYC demonstrating against police brutality and the group formally disavowed them.
"We are going to have to, perhaps, talk to the attorney general about it or do something," Trump said when O'Reilly asked if Trump would order his attorney general to investigate the group.
"At a minimum, we're going to have to be watching because that's really bad stuff and it's happened more than once," he said.
Trump's comments came as the Republican National Convention
got underway, and at the same time as the mother of an American killed in the attack on the US consulate in Benghazi addressed the convention.
The interview also came after Trump's team beat back the latest -- and likely last -- challenge to his nomination earlier Monday in a rowdy scene on the convention floor -- an image that cast a shadow on continued hopes for a unified Republican Party.
Trump also addressed Ohio Gov. John Kasich's
apparent decision not to appear
at the GOP convention, saying that the governor signed a pledge during the primaries to support the GOP nominee and should show up regardless as the governor of the convention's host state.
"Look, I beat him very badly," Trump said. "If I were him and gotten beaten that badly, I probably wouldn't show up either. He has a problem though. He signed the pledge. And from a standpoint of honor, I think he should show up."
But, perhaps in the convention's spirit of GOP unity, Trump declined to call Kasich a sore loser.
"Well, I don't want to say that," Trump demurred.