In the interview with Bloomberg TV anchor Stephanie Ruhle, Trump did not directly blame Bush for the attacks.
Still, his remarks are sure to reverberate in GOP circles, especially given his rivalry with Jeb Bush — the former president's brother.
The topic came up when Ruhle raised a question near the end of her interview with Trump about leadership, and how some leaders have shown a softer touch. 
She noted that President George W. Bush stood in front of the country after the 9/11 attacks, and that President Obama did so following the Sandy Hook school shooting that left 26 people dead in 2012.
"Help us understand who Donald Trump is as a man. I need to know that you will make us feel safe and you will make us feel proud," she said.
"I think I have a bigger heart than all of them. I think I'm much more competent than all of them," Trump responded. "When you talk about George Bush – I mean, say what you want, the World Trade Center came down during his time."
"Hold on, you can't blame George Bush for that," Ruhle interjected.
Trump shrugged a bit.
"He was president, OK? ... Blame him or don't blame him, but he was president. The World Trade Center came down during his reign," Trump said.
"If you look at Sandy Hook, those people are still begging for help. It's a disaster, and it's a disaster all over the place," he continued.
"Government has proven to be a disaster during the Obama administration. I think I have a bigger heart than all of them, and I think I'm much more competent than them," Trump said. "And we will be great again. This country will be great again. We have tremendous potential, we have tremendous people. What we need is a leader, we don't have a leader."
Bush shot back at Trump in a tweet, calling the businessman "pathetic."
Trump is currently the front-runner for the Republican nomination in a race that includes former Florida Gov. Jeb Bush, George W. Bush's brother.
Bush slammed Democratic candidate Hillary Clinton last month over an advocacy group's ad implying his brother did not keep the nation safe while president.