Black was also quoted as saying the assassination of Benazir Bhutto, the former Pakistani prime minister, in December 2007, "helped us".
When questioned about Black's comments during a news conference, McCain said: "I cannot imagine why he would say it; it's not true. I've worked tirelessly since 9/11 to prevent another attack on the United States of America. My record is very clear."
A McCain campaign official said Black did not remember making the particular comment to Fortune but did not dispute the characterisation.
The official said what Black meant was that a focus on national security issues was good for McCain.
The campaign of Barack Obama, the Democratic candidate, condemned the remark, calling it a "complete disgrace".
"The fact that John McCain's top adviser says that a terrorist attack on American soil would be a 'big advantage' for their political campaign is a complete disgrace, and is exactly the kind of politics that needs to change," said Bill Burton, an Obama spokesman.
John Kerry, the Massachusetts senator who lost to George Bush in the 2004 election, said Black's comment smacked of "the worst of the Rove-Bush fear playbook", a reference to Bush's former political adviser, Karl Rove.
In the 2004 presidential race, Dick Cheney, the vice-president, and other Republicans argued Kerry was weak on national security, an argument that resonated with voters at the polls.
The Republicans also questioned the Democrats' record on national security in 2002, and it paid dividends at the polls in the congressional elections.