Tripoli, Libya (CNN) -- One of Libyan leader Moammar Gadhafi's sons -- Saif al-Arab Gadhafi -- was killed after a NATO airstrike, a spokesman for Libya's government said Sunday at a press conference.

Moammar Gadhafi and his wife were in their son's house when it was targeted, spokesman Musa Ibrahim said. Both of them are in good health, according to the spokesman.

The victim is one of two Gadhafi sons whose names begin with Saif. The other is Saif al-Islam Gadhafi, who had previously touted reform but has emerged as one of his father's most visible defenders in recent months.

Ibrahim said several of Moammar Gadhafi's grandchildren also died in the attack.

The house in Tripoli was destroyed by the strike, with a massive crater where the house used to be. At least one unexploded bomb could be seen.

The building was in a residential area of Tripoli, according to Ibrahim, who insisted that Saif al-Arab Gadhafi was a student in Germany who was not deeply involved in Libya's military and government. The 29-year-old was the sixth of Gadhafi's eight biological children.

Ibrahim railed against NATO after the fatal strike, calling it an illegal act and a "war crime."

Lt. Gen. Charles Bouchard, commander of NATO's military operations, said in a statement 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," Bouchard said. "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, while a large crowd of demonstrators gathered around Moammar Gadhafi'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," as well as, "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.

A spokesman for the Libyan opposition doubted the veracity of the report of the son's death, saying, "In all honesty, we never heard of Saif al-Arab until the start of the uprising."

"We don't believe this is true," said Abdul Hafiz Ghoga, deputy chairman of the Transitional National Council in Benghazi. "It is all fabrications by the regime in a desparate attempt to get sympathy ... This regime constantly lies and keeps lying."

Ibrahim, the spokesman for Gadhafi's government, accused NATO of launching the strike specifically in order to kill the Libyan leader.

Earlier this week, U.S. Ambassador to Libya Gene Cretz acknowledged that "our own laws" would affect any decision to try to assassinate Moammar Gadhafi directly.

"I don't believe that any credible group or individual sees the solution to the Libyan problem without the removal of Moammar Gadhafi, one way or the other," he said. "But our job and our goal is to get a political solution, but through the means that we are allowed to by our own laws."

This is not the first time that Moammar Gadhafi reportedly has been at the site of an airstrike that killed one of his children.

In April 1986, U.S. forces launched an airstrike that targeted Moammar Gadhafi's residential compound. As a result, the Libyan leader's adopted daughter, Hanna Gadhafi, was killed.

Saif al-Arab Gadhafi, then just 3 years old, was hospitalized after suffering injuries in that strike, Libyan officials then said. Video shows what Libyan officials claimed were him and his brother Khamis, though both boys were heavily bandaged and their faces were not clearly visible.

At the time, President Ronald Reagan told the American people the bombings were an act of self-defense following the bombing of a West Berlin club that killed two American servicemen and injured several others.

And on Monday, Ibrahim issued a defiant statement saying Moammar Gadhafi was alive despite what the Libyan government called a NATO attempt to kill him by bombing his compound.

"The message that was sent by NATO in the early hours of this morning was sent to the wrong address," Ibrahim said.

Bruce Riedel, a former adviser to three U.S. presidents and now a senior fellow at the Brookings Institution think tank, said the reported killing could complicate any chances that Moammar Gadhafi might leave Libya peaceably after a negotiated solution.

"A political solution was always a long shot," Riedel told CNN by e-mail. "But in Libya's very tribal politics, the death of a son makes any political settlement all that much harder."

CNN's Phil Gast and Kareem Khadder contributed to this report.