An adviser to John McCain who claimed that a terrorist attack would be a "big advantage" for his candidate has dropped off the campaign trail, at least temporarily.

Meanwhile, Barack Obama's camp continued Tuesday to lambaste Charlie Black for the remarks published in Fortune magazine.

"One, I think factually he’s wrong," Obama said Tuesday evening. "The broader point which has been made not just by Democrats but by Republicans is there are certain things that should transcend politics, and I think the prospect of a terrorist attack on American soil is one of them."

Black, a key foreign policy strategist for the likely Republican presidential nominee, apologized for the comments on Monday. Fortune quoted Black saying of a terror attack on U.S. soil: “Certainly it would be a big advantage to him.”

McCain also condemned his adviser, saying, "I cannot imagine why he would say it, it's not true ... I strenuously disagree."

But after accompanying McCain on the campaign trail Monday, Black was nowhere to be seen Tuesday.

Asked if Black should be fired, Obama said, "I leave it up to John McCain as to who he wants to run his campaign."

Still, the Obama campaign circulated a report from the Think Progress Web site Tuesday revisiting similar comments McCain made during the 2004 election.

Shortly before that election, McCain was quoted saying that the latest Usama bin Laden video message would be "very helpful" to President Bush because it focused voters' attention on the War on Terror -- considered at the time to be Bush's strong suit.

Black's recent comments to Fortune were also made while discussing McCain's national security credentials. He said McCain’s support grows when public attention turns to disasters like the December assassination of former Pakistan Prime Minister Benazir Bhutto.

Black called Bhutto’s death an “unfortunate event,” according to the article published Monday. “But his knowledge and ability to talk about it re-emphasized that this is the guy who’s ready to be commander-in-chief. And it helped us.”

The Obama campaign held a conference call Tuesday with former Sept. 11 commission member Richard Ben Veniste and policy adviser Denis McDonough, who assailed Black for his comments.

McDonough called for a debate on who would better protect the country, instead of using the "politics of fear."

"We’ve seen the political play that was manifest yesterday by Mr. Black’s candid comments, so what we want to do is get back to what will make this country safer," he said. "That has not been the record of this administration or what Senator McCain appears ready to continue for the next four years."

McDonough, however, stopped short of saying that Black's comments indicate that his boss shares his notion of the political benefits of a terror attack.

Ben Veniste wouldn't call for McCain to fire his trusted adviser, saying only that Black's remarks "call for some recalibration in the thinking and perhaps a greater adherence to principle here in staying away from the politics of fear, and I would suggest it would be a good idea to caution those whose candid thoughts have created this turmoil with Senator McCain."

Neither official would comment on how Black's remarks were different than Hillary Clinton's last August, when the New York senator and former Obama rival said that a terrorist attack could help the GOP and that she was the best Democrat to counter that political impact.

FOX News' Mosheh Oinounou and Aaron Bruns contributed to this report.