Tripoli, Libya (CNN) -- The Libyan government said Sunday that ruler Moammar Gadhafi's son and three of his grandchildren died in a NATO airstrike that the longtime strongman and his wife survived.
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. But the son, Saif al-Arab Gadhafi, and three of his children were killed, Ibrahim said.
The Libyan government vowed to retaliate with death to "invaders" in the nation, and empty Western embassies were vandalized on Sunday, U.S. and Italian officials said. But CNN could not independently confirm the reported fatalities, and a spokesman for anti-Gadhafi rebels cast doubt on the claim even as it provoked celebratory gunfire in rebel-held Benghazi.
Ibrahim slammed NATO after the airstrike, calling the attack an illegal act and a "war crime." He said the 29-year-old son killed was a student in Germany, the sixth of eight children. The strike destroyed the house in Tripoli, leaving a massive crater.
Saif al-Arab Gadhafi is one of two sons of the Libyan leader whose names begin with Saif. 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 commander of the NATO operation, Lt. Gen. Charles Bouchard, said NATO was aware of "unconfirmed media reports" that members of Gadhafi's family had been killed in an airstrike.
"We regret all loss of life, especially the innocent civilians being harmed as a result of this ongoing conflict," said Bouchard, a Canadian air force general. But he said 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."
But Russia, which has criticized the allied campaign, said it had "serious doubts" about NATO's assertion that it is not targeting Gadhafi and his family.
"The disproportional use of force, all the more so, beyond the mandate of U.N. Security Council Resolution No. 1973, which in no way stipulates the replacement of the Libyan leadership, is leading to harmful consequences and the death of civilians," the Russian Foreign Ministry said in a statement carried by the official RIA Novosti news agency. "We are again calling for strict compliance with the provisions of the decisions made by the international community on the Libyan conflict, for an immediate cease-fire and the start of a political settlement without any preconditions."
The airstrikes started March 19, after the U.N. Security Council approved a resolution authorizing the use of force to protect civilians demanding the ouster of the ruler, who has been in power for nearly 42 years.
A senior official in President Barack Obama's administration said the U.S. government is "very aware" of the reports of Gadhafi's son's death, 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.
A spokesman for the Libyan opposition doubted the report of the death.
"In all honesty, we never heard of Saif al-Arab until the start of the uprising," said Hafiz Ghoga, deputy chairman of the Transitional National Council in Benghazi.
"We don't believe this is true," Ghoga said. "It is all fabrications by the regime in a desperate attempt to get sympathy. ... This regime constantly lies and keeps lying."
Despite skepticism by some rebels, some opposition members celebrated the report of Saif al-Arab's death in the streets of Benghazi.
Revelers danced and sang overnight as the sound of celebratory gunfire pierced through the air.
"By God, we're not supposed to rejoice anyone's death," one man told CNN. "But we want him to feel the pain and sorrow that we're going through with our own people he killed."
Many of the reported civilian deaths have come out of the western city of Misrata. On Sunday, a witness there described especially intense shelling by government forces in the country's third-largest city and speculated that the intensified attacks were tied directly to reports of the death of Gadhafi's son.
This is not the first time the ruler has reportedly been at the site of an airstrike that killed one of his children.
In April 1986, his adopted daughter, Hanna Gadhafi, was killed when U.S. forces launched an airstrike that targeted his residential compound.
At the time, U.S. President Ronald Reagan said the strikes were an act of self-defense following the bombing of a West Berlin, Germany, club that killed two American servicemen and injured several others.
CNN's Reza Sayah, Kareem Khadder, Saad Abedine and Phil Gast and contributed to this report.