WASHINGTON — Iran’s support for Al Qaeda is flaring up as an issue in the American presidential campaign.

Senator Obama, in a speech marking the fifth anniversary of the Iraq War, criticized Senator McCain, saying the Republican presidential candidate had confused Iran and Al Qaeda and Sunnis and Shiites in remarks Mr. McCain made Tuesday. Mr. McCain, in a subsequent statement, stuck to his guns, saying, “Al Qaeda and Shi’ia extremists — with support from external powers such as Iran — are on the run but not defeated.”

In Amman on Tuesday, Mr. McCain said that Iranian operatives had trained Al Qaeda in Iran and helped them re-enter Iraq. Seconds later, after Senator Lieberman, an independent Democrat from Connecticut, whispered in his ear, Mr. McCain said, “I’m sorry, the Iranians are training extremists, not Al Qaeda.”

But while the McCain campaign is backing away from the specific claims about Iranian training of Al Qaeda, it is asserting that Iran collaborates with Osama bin Laden’s organization.

Mr. McCain’s national security adviser, Randy Scheunemann, told The New York Sun, “There is ample documentation that Iran has provided many different forms of support to Sunni extremists, including Al Qaeda as well as Shi’ia extremists in Iraq. It would require a willing suspension of disbelief to deny Iran supports Al Qaeda in Iraq.”

Responding to Mr. Scheunemann’s remarks, a senior foreign policy adviser to Senator Obama, Susan Rice, yesterday told the Sun, “It’s very bizarre.” She noted that Mr. McCain had “made the same statement three times in as many days. Surely he must know, as Senator Lieberman reminded him, that Iran is not engaged with Al Qaeda in Iraq. I don’t know if he is confused, or is he cynically trying to conflate Al Qaeda and Iran as Cheney and Bush did Al Qaeda and Iraq in 2002 and 2003?”

Ms. Rice stipulated in the interview that she was not saying Iran and Al Qaeda have never worked together, but that “there is no body of evidence to suggest Iran is aiding Al Qaeda in Iraq.”

The Sun, in a series of dispatches from northern Iraq and Baghdad, detailed claims that Iran has supported Al Qaeda in Iraq. One such dispatch, published on April 25, 2007, quoted the director of the security ministry for the Sulaimaniyah province, Sarkawt Hassan Jalal, as saying Iran had harbored the leadership of a group calling itself Al Qaeda in Kurdistan in five towns on the Iraqi border. A subsequent story, based on an interview with a Kurdish prisoner who went by the name Osman the Small, said Iran’s revolutionary guard and domestic intelligence service had issued the Kurdish jihadist group political refugee cards, identifications that made it possible for them to cross back and forth into Iraq from Iran.

Senior military officials from Multinational Forces in Iraq have said on the record that Iran provides support for Sunni terror outfits in Iraq, but they have not identified them as Al Qaeda in Iraq. A former commander of a group that has at times aligned with Al Qaeda in Iraq, the Islamic Army of Iraq, Abu Azzam al Tamimi, told Al Arabiya television on January 18, 2008, that Iran “interferes in every aspect in Iraq.” When asked whom Iran supports, Mr. al Tamimi said, “Everybody — it works with the government, with the opponents of the government, with the opponents of the government’s opponents, with Al-Qaeda, with the enemies of Al-Qaeda, with the militias, with the enemies of the militias … Iran spreads its investments everywhere – with the Shiites, the Sunnis, and the Kurds,” according to a translation by the Middle East Media Research Institute.

The Sun also reported in July that a senior leadership or management council for Al Qaeda meets regularly in eastern Iran, according to the classified portion of the latest national intelligence estimate on Al Qaeda. An intelligence briefer to the press for that estimate at the time claimed to have no recollection of the section, but the Sun maintains that it is there. Following the defeat of Al Qaeda in Afghanistan in 2001, many senior Al Qaeda leaders, such as Saif al Adel and Saad bin Laden, fled to Iran, while others, such as Osama bin Laden and Ayman al Zawahiri, are believed to have fled to the border tribal provinces in Pakistan.

Senior Bush administration officials have in the past said as much. In a 2005 interview with NBC News, the president’s homeland security adviser, Frances Townsend, said, “We believe that they’re holding members of Al Qaeda’s management council.” She went on: “And we have encouraged and suggested that they ought to try them, they ought to admit freely that they’re there — which they have not done — that they’re holding them. Or they ought to return them to their countries of origin, which they’ve also been unwilling to do.”

The status of men such as Mr. al Adel is described as a “form of house arrest.” But in 2003 during negotiations between America and Iran to examine a swap for anti-Iranian terrorists known as the People’s Mujahedin for the senior Al Qaeda leaders, Saudi Arabia provided an intercept of Mr. al Adel in communication with an Al Qaeda cell in Riyadh that planned a series of bombings in May of that year. The New York Times reported at the time that the Bush administration believed it had “rock-hard” evidence of at least 12 Al Qaeda leaders “directing some operations from Iran.”

And the final report of the National Commission on Terrorist Attacks Upon the United States said, “Intelligence indicates the persistence of contacts between Iranian security officials and senior Al Qaeda figures after Bin Ladin’s return to Afghanistan. Khallad has said that Iran made a concerted effort to strengthen relations with Al Qaeda after the October 2000 attack on the USS Cole, but was rebuffed because Bin Ladin did not want to alienate his supporters in Saudi Arabia. Khallad and other detainees have described the willingness of Iranian officials to facilitate the travel of Al Qaeda members through Iran, on their way to and from Afghanistan. For example, Iranian border inspectors would be told not to place telltale stamps in the passports of these travelers. Such arrangements were particularly beneficial to Saudi members of Al Qaeda.”

The report went on, “we now have evidence suggesting that 8 to 10 of the 14 Saudi ‘muscle’ operatives” who were perpetrated the September 11 attacks for Al Qaeda “traveled into or out of Iran between October 2000 and February 2001.”