The Washington Post reported on Tuesday that Saad bin Ladin is part of a small group of leaders running the group with Iran's backing.
Citing intelligence sources, the newspaper said bin Ladin's eldest son was in contact with an al-Qaida cell in Saudi Arabia prior to a May bombing attack in Riyadh that killed 35 people.
The sources said their contacts led them to conclude the attacks were planned in Iran and ordered from there.
The newspaper said Saudi Arabia had been trying to persuade Iran to extradite bin Ladin and other suspects in the bombing.
Saudi officials estimate there are up to 400 al-Qaida members in Iran.
But Muhammad Iskandari, of the Iranian embassy in London, vehemently denied Saad bin Ladin was in Iran.
He said: "These claims are untrue. Iran is at the forefront of the campaign against terrorism. We have expelled 2300 people without valid identity documents from our borders, we have handed over 100 al-Qaida suspects, and we are going to prosecute more."
"Iran is at the forefront of the campaign against terrorism. We have expelled 2300 people without valid identity documents from our borders, we have handed over 100 al-Qaida suspects, and we are going to prosecute more"
Iranian embassy, London
And Iskandari said the timing of the Washington Post story - weeks before Iran has to prove it is not developing nuclear weapons - was highly suspect.
"The US and the Zionist regime are using all their efforts to put pressure on Iran," he said.
"With regard to the nuclear allegations, their suspicions are baseless. It is like when they said there were weapons of mass destruction in Iraq but nothing was found."
Born in Saudi Arabia, Saad bin Ladin is believed to be 24 years old and is one of the eldest sons of Usama bin Ladin and his first wife.
Bin Ladin's children
Bin Laden has more than two dozen children from several marriages.
According to The Washington Post, Saad was at his father's side in Afghanistan in the mid-1980s when al-Qaida was formed, and was groomed to take a leadership role.
The younger bin Ladin has only recently emerged as an important target for the CIA and FBI.