He was responding to a charge by Barack Obama's campaign that his party has been politicising the attack, which resulted in the death of the US ambassador to Libya and three other Americans.
He said it was an issue in the presidential campaign as Americans wondered why the Obama administration took so long to acknowledge it was a terrorist act.
At a rally in North Carolina, the Republican candidate read aloud comments from Obama spokeswoman Stephanie Cutter about the attack.
Ms Cutter had said: "The entire reason that this has become the political topic it is is because of Mitt Romney and Paul Ryan."
Mr Romney said: "No, president Obama. It's an issue because this is the first time in 33 years that a United States ambassador has been assassinated.
"Mr President, this is an issue because we were attacked successfully by terrorists on the anniversary of September 11.
"President Obama, this is an issue because Americans wonder why it was it took so long for you and your administration to admit that this was a terrorist attack."
In response, Obama campaign spokeswoman Lis Smith said Mr Romney was trying to "score cheap political points".
The back-and-forth came a day after Republicans confronted State Department officials about security at the US consulate in Libya and attacked the Obama administration's early response to the Libya assault.
Ambassador Chris Stevens died in what administration officials now describe as an act of terrorism.
In statements immediately after the attack, neither Mr Obama nor secretary of state Hillary Clinton mentioned terrorism, though Mr Obama referred to "acts of terror" in his Rose Garden statement the morning after the assault.
Both Mr Obama and Ms Clinton gave credence to the notion the attack was related to protests about an anti-Islam video.
Ms Clinton said on the night of the attack: "Some have sought to justify this vicious behaviour as a response to inflammatory material posted on the internet.
"The United States deplores any intentional effort to denigrate the religious beliefs of others. Our commitment to religious tolerance goes back to the very beginning of our nation.
"But let me be clear: There is never any justification for violent acts of this kind."
Mr Romney's latest criticism came as Vice President Joe Biden and the man who wants to succeed him, Republican Paul Ryan, clashed in a feisty debate over foreign and economic policy.
Mr Biden also sought to make up for President Barack Obama's lacklustre performance against Mr Romney last week.
The two went head-to-head over the Obama administration's policy in Libya and Iran in the opening minutes of the debate, with Mr Ryan claiming it is weakening America's standing in the world. He said the death of the US ambassador was evidence that the administration's foreign policy was unravelling.
Mr Biden reminded viewers Mr Obama was willing to chase the September 11 terrorist mastermind Osama bin Laden to the end of the earth.
Mr Romney and Mr Obama meet again on Tuesday for a town hall-style debate in New York.