The feud between Republican presidential rivals Donald Trump and Jeb Bush is growing increasingly personal, even though the real estate mogul and primary front-runner insisted on Sunday that he did not mean to blame Bush's brother, former President George W. Bush, for the Sept. 11, 2001, terror attacks.

"I'm not blaming anybody, and I'm not blaming George Bush," Trump said in a Fox News interview that aired on Sunday. But the New York native did suggest that the then-president was responsible for what he sees as a wide array of intelligence and immigration policy failures that contributed to the unprecedented attack on the city's World Trade Center, as well as the Pentagon outside Washington, D.C.

"The fact is we had the worst attack in the history of our country during his reign. Jeb (Bush) said we were safe during his reign. That wasn't true," Trump said. And the U.S. intelligence community, meanwhile, was in disarray at the time, he charged. "If you look at his three primary agencies, they hated each other, they weren't talking. And a good leader would've made sure that they would get along and talk and lots of other things happen."

The GOP frontrunner also questioned whether the foreign al-Qaeda terrorists who perpetrated the hijackings on Sept. 11 would have even been present in the United States had he occupied the White House at the time, Politico noted.

"I am extremely, extremely tough on people coming into this country," Trump said. If he had been president, he doubted "those people would've been in the country. ... There's a good chance that those people would not have been in the country," the 69-year-old speculated.

But also over the weekend, Bush took to defending his brother on CNN's "State of the Union" Sunday morning show.

"My brother responded to a crisis, and he did it as you would hope a president would do -- united the country, he organized the country and he kept us safe," Bush said. "There's no denying that and the great majority of Americans believe that, and I don't know why he keeps bringing this up."