Gadhafi and his wife were in their son’s house when it was targeted, but they are in good health, government spokesman Musa Ibrahim told journalists.
In addition to Saif al-Arab Gadhafi, three of the ruler’s grandchildren also died in the attack, he said.
CNN could not independently confirm the reports.
Saif al-Arab Gadhafi is one of two sons whose names begin with Saif. The 29-year-old is the sixth of his eight biological children.
Another son — Saif al-Islam Gadhafi — had previously touted reform, but has emerged as one of his father’s most visible defenders in recent months.
The strikes destroyed the house in Tripoli, leaving a massive crater where it used to be.
The building was in a residential area of the capital, according to Ibrahim, who said the son killed was a student in Germany.
Ibrahim slammed NATO after the airstrike, calling it an illegal act and a “war crime.”
A NATO official said in a statement Sunday that he was “aware of unconfirmed media reports that some of Gadhafi’s family members may have been killed.”
“We regret all loss of life, especially the innocent civilians being harmed as a result of this ongoing conflict,” said Lt. Gen. Charles Bouchard, commander of NATO’s military operations.
“NATO is fulfilling its U.N. mandate to stop and prevent attacks against civilians with precision and care — unlike Gadhafi’s forces, which are causing so much suffering.”
The NATO commander stated that all targets “are military in nature and have been clearly linked to the Gadhafi regime’s systemic attacks on the Libyan population … We do not target individuals.”
A senior official in President Barack Obama’s administration said the U.S. government is “very aware” of the reports, but cannot confirm who, if anyone, died in a strike until they see the evidence.
Gunfire broke out around Tripoli after the news came out. A crowd of demonstrators gathered around the ruler’s compound. Images on Libyan state TV showed what appeared to be dozens of people chanting and waving flags.
Protesters could be heard yelling, “We want to redeem the martyr,” and, “Oh youth, this is time for jihad.”
They were joined at one point by Ibrahim, who told the demonstrators, “Every one of you are Saif al-Arab.”
“We will make Libya the grave of all invaders,” he told the crowd.
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