Frustrated by evasion and resilience of Qadhafi's military, Nato has pledged to step up its strikes on the broader instruments of his power.

The government of Muammar Qadhafi said he survived an airstrike in Tripoli late Saturday night that killed one of his sons and three grandchildren, in the sharpest intensification yet of the Nato air campaign intended to pressure the Libyan leader from power.

The son, Seif al-Arab Muammar Qadhafi, 29, and the grandchildren, all said to be younger than 12, were possibly the first confirmed casualties in the airstrikes on the Libyan capital. And while the deaths could not be independently verified, the campaign against Libya's most densely populated areas raised new questions about how broadly Nato is interpreting its United Nations mandate to protect civilians.

It is the second airstrike in seven days to hit a location intimately close to the Libyan leader, following a midnight attack last week that destroyed an office building in his compound where he and his aides sometimes work.

In a news conference early Sunday in Tripoli, a Qadhafi government spokesman called the strike an illegal attack. “This was a direct operation to assassinate the leader of this country,” said the spokesman, Musa Ibrahim. “This is not permitted by international law. It is not permitted by any moral code or principle.” He said Mr. Qadhafi and his wife, who were staying at the house along with “friends and family,” were not hurt.

American and Nato officials have said they are not seeking to kill Mr. Qadhafi, and some have suggested it might not be very easy. But frustrated by the evasion and resilience of Mr. Qadhafi's military, Nato has pledged to step up its strikes on the broader instruments of his power, including state television facilities and command centres in the capital.

In a news release, the Nato mission's operational commander, Lt. Gen. Charles Bouchard, said he was aware of the reports of Qadhafi family deaths but called them unconfirmed. He added: “All Nato's targets are military in nature and have been clearly linked to the Qadhafi regime's systematic attacks on the Libyan population and populated areas. We do not target individuals.”

A Nato official in Naples, Italy, reached by e-mail and responding on the condition of anonymity, said allied planners had not known that Mr. Qadhafi's family members were in the building that was attacked, which the official described as a command and control centre. The official would not specify the nationality of the aircraft or pilots that carried out the strike.

In a video broadcast by the satellite channel Al-Jazeera, Libyan officials showed reporters what they said was the destroyed house, a large crater, crumbled concrete and twisted metal, and someone dusting off what appeared to be an unexploded bomb. 

It is not the first time Mr. Qadhafi has survived such a close call. In 1986, the U.S. struck his compound in retaliation for a terrorist attack on a German nightclub frequented by U.S. service members. Mr. Qadhafi has incorporated his survival into his cult of personality, preserving the wreckage of the building as a “Museum of Resistance” and erecting a statue of a giant fist grabbing an American warplane.

Although several of Mr. Qadhafi's seven sons and one daughter play major roles in the Libyan economy and government (including an older brother with a similar name, Seif al-Islam Qadhafi), the son reported killed had been considered a black sheep, believed to spend much of his time in Munich. Many Libyans said they had never seen his picture. 

In Benghazi, the de facto rebel capital in eastern Libya, and in Misrata, a western city that Mr. Qadhafi's forces have besieged for months, celebratory gunfire rang out and explosions could be heard.

But even then, doubts lingered in Benghazi about whether the news was true:  In interviews, residents said they were happy but suspected a ploy by Mr. Qadhafi to win sympathy. Ramadan el-Sheikhy, who said his brother was killed in one of Mr. Qadhafi's prisons, said any sympathy was misplaced. “I was happy at the news,” he said. “Hopefully, he felt the pain of having a relative killed.” 

Earlier on Saturday, Nato officials had rejected an offer by Mr. Qadhafi to call a ceasefire and negotiate as false. The proposal was delivered in a rambling and often defiant speech, broadcast over Libyan state television, in which Mr. Qadhafi insisted he would never leave Libya. “Come France, Italy, U.K., America, come, we'll negotiate with you,” he said. “You lie and say I'm killing my own people. Show us the bodies.”

The speech, which was broadcast about 2:30 am, was the latest in a series of proclamations from the Libyan leader, and it was made as Nato forces said they would broaden their list of targets to include palaces, communication centres and other administrative buildings that Mr. Qadhafi relies on to maintain power.

Nato and the rebels immediately rejected the call for a ceasefire, which they described as a disingenuous ploy. Mr. Qadhafi repeated his assertions that the rebels belonged to the al-Qaeda or were terrorists and mercenaries, even as he appealed to them to lay down their weapons.

Looking relaxed as he sat behind a desk, and gazing at someone or something off camera, he lost his train of thought several times and referred to notes in his hand. “Qadhafi doesn't have the power, he doesn't have the position to leave,” he said of himself. “With my rifle, I will fight for my country.”

An opposition spokesman in Benghazi, Jalal al-Gallal, dismissed Mr. Qadhafi's offers as “public relations for the world.”

“We know he's not being genuine,” al-Gallal said. “He's not once offered anything and followed through.”

There were few signs that he intended to ease the military pressure on his opponents. A rebel military spokesman said Qadhafi forces had begun an assault early Saturday on the eastern towns of Jalu and Awjilah, about 120 miles south of Ajdabiya, attacking in trucks mounted with anti-aircraft guns and Grad rockets. The spokesman, Col. Ahmed Omar Bani, said five civilians had been killed in the fighting and 10 had been wounded.

The attack, which could not immediately be confirmed, seemed to follow an emerging pattern in the conflict in which the rebels have stepped up their resistance in the west in the Nefusa mountain region, along the Tunisian border and in the strategic port city of Misrata. At the same time, Mr. Qadhafi's forces have made harassing raids on poorly defended towns near the eastern oil fields in recent weeks, at times straining the rebels' efforts to keep producing oil.

A stalemate persisted on the country's main coastal road near the city of Brega, which was the site of intense fighting for weeks. Col. Bani said there had been few skirmishes over the past two weeks on the front there, which lies between Brega and Ajdabiya, about 45 miles to the east.

The rebels have said that in the coming days, they will appoint a new defence minister to replace Omar al-Hariri, a former political prisoner who occupied a largely ceremonial role in the rebels' transitional government. They were hoping the appointment of a civilian would impose a measure of organisation on an inexperienced fighting force that has been plagued by setbacks on the eastern front and infighting in its upper ranks. Fighting continued for Misrata, and early Saturday, large explosions on the outskirts shook the coastal city. Rebels later said they were Nato airstrikes.

The pro-Qadhafi forces resumed shelling and firing rockets into the city in the morning, and again late at night. At least 15 people were reported killed, including at least five rebel fighters, an old man who was struck by shrapnel, and a young father of four children.

(Kareem Fahim reported from Benghazi, and David D. Kirkpatrick from Cairo. C.J. Chivers contributed reporting from Misrata, Libya.) — New York Times News Service

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