While defending his administration's record on security matters, President Obama told reporters in Washington Graham was "not right on this issue."
But Graham, in a telephone interview from Phoenix with CNN, cited the deaths of four Americans at the U.S. Consulate in Benghazi, Libya, and four in the Boston Marathon bombings and aftermath at the hands of "radical Islamists" as evidence "our systems are degrading and I stand by that statement."
"It's not like I relish saying that. I just think it's true," Graham, a member of the Senate Armed Services Committee, said.
He said the consulate "became a death trap for 7 1/2 hours" because multiple warnings from Ambassador Christopher Stevens, one of the four killed in Benghazi, were "ignored" and requests for security were "denied."
Graham faulted gaps in the intelligence system that put slain Boston Marathon bombing suspect Tamerlan Tsarnaev on the radar only to fail to foil the attack.
"A guy that's already in the system that's suspected to be a radical Islamist is now on the Web inside the United States, embracing radical Islamist ideology and the rest is history," Graham said.
"Our systems are failing, in my view."
Graham said he wants a joint select committee of Congress to re-examine what happened at Benghazi "because there are people now alleging they want to come forward, but are afraid to do so." He said he wants another joint select committee to look at the FBI, the CIA and the Department of Homeland Security regarding the Boston attack.
"It's not so much about blaming people as to get it right," he said. "We've lost eight Americans in seven months, four overseas, four at home. We need to up our game."