The tycoon takes aim at Republican rival Jeb Bush as he insists his tough stance on immigration would have kept America safe.
Donald Trump has claimed the 9/11 attacks on the World Trade Centre and the Pentagon probably would not have happened if he had been President.
In an interview with Fox News, the real estate billionaire said if he had "been running things" his tough stance on immigration would have meant "a good chance" that the plane hijackers "would not have been in our country".
The comments come amid growing tensions between Mr Trump and one of his rivals for the Republican presidential nomination, Jeb Bush.
Mr Trump has repeatedly tried to attack Mr Bush by forcing him to defend his brother George W Bush’s security record while in office, and criticising him for taking America to war in Iraq.
Jeb Bush has adopted a four-word riposte in defence of his brother - "He kept us safe" - which has gained applause from debate audiences.
However, in his appearance on Fox News Sunday, Mr Trump said: "Jeb said we were safe with my brother, we were safe. Well the World Trade Centre just fell down.
"Now am I trying to blame him? I'm not blaming anybody. But the World Trade Centre came down, so when he said we were safe, that's not safe."
Asked how Mr Trump would have done things differently, he said: "I am extremely, extremely tough on immigration. I'm extremely tough on people coming into this country.
"I believe that if I were running things, I doubt those families would have - I doubt that those people would've been in the country."
All but one of the 19 men who hijacked the four planes involved in the attacks entered the country legally either on business, student or tourist visas.
Responding to Mr Trump's comments, Jeb Bush said in a CNN interview: "Does anyone actually blame my brother for the attacks on 9/11? If they do, they're totally marginalised in our society.
"It’s what he did afterwards that matters, and I'm proud of him."
Mr Bush also hit back at the former reality TV star, saying: "Across the spectrum of foreign policy, Mr Trump talks about things as though he's still on The Apprentice."
The former Governor of Florida, who trails Mr Trump in the polls, also released this video lampooning the property tycoon's grasp on foreign policy.
However, the man who prefers to be known as Jeb! (always with an exclamation mark) is failing to inject excitement into his campaign.
The latest Fox poll has Mr Trump leading the field of 15 remaining candidates with Mr Bush in fifth place, also behind Ben Carson, Ted Cruz and Marco Rubio.
source: Donald Trump: I Could Have Prevented 9/11
Hindsight is 20/20