Nato is facing urgent questions about the legality of its air strike on a Gaddafi family compound at the weekend, which the Libyan government said had killed the leader's second youngest son, 29-year old Saif al-Arab, and three grandchildren under 12. The grandchildren were not named.
The Libyan government spokesman, Moussa Ibrahim, said Muammar Gaddafi and his wife, Safiya, had been in the building at the time, but had escaped injury. He said the aim of the attack was clear: to assassinate the Libyan leader.
Nato swiftly scrambled to deny that it was targeting any individuals, insisting that it was only interested in attacking the military command structure.
The prime minister, David Cameron, told the BBC that UN resolutions permitted attacks against the regime's "command and control" sites because their aim was to prevent "a loss of civilian life by targeting Gaddafi's war-making machine".
But the deaths of Gaddafi's three grandchildren, if confirmed, will reinforce the doubts of alliance members uncomfortable with Nato's six-week bombing campaign and generate criticism from countries such as Russia that Nato is pushing beyond its UN security council mandate.
"Statements by participants in the coalition that the strikes on Libya are not aimed at the physical destruction of ... Gaddafi and members of his family raise serious doubts," the Russian foreign ministry said. "The disproportionate use of force ... is leading to detrimental consequences and the death of innocent civilians." The ministry called for "an immediate ceasefire and the beginning of a political settlement process without preconditions."
The Venezuelan president, Hugo Chávez, said in Caracas: "There is no doubt the order was given to kill Gaddafi. It doesn't matter who else is killed … this is a murder."
The attack, which one diplomatic source said had been carried out by Danish airmen possibly in an F16 bomber, ripped through the Gaddafi residence at around 8pm on Saturday night. It was the second time in recent days that an airstrike has come close to the Libyan leader, and Ibrahim indicated that someone within the leader's circle may have leaked intelligence on his whereabouts.
But in Washington, Stephen Hadley, former national security adviser in the Bush administration, warned that the assassination of Gaddafi by Nato aircraft could prove counterproductive.
"The narrative we want to come out of this is that the Libyan people overthrew a dictator – not that we came in and toppled a despot," he told CNN. "What we really want him to do is to leave or to die at a Libyan hand, not an American hand."
But senior Republicans expressed little concern over the prospect of Gaddafi becoming a casualty. Senator Lindsey Graham told Fox News: "Wherever Gaddafi goes, he is a legitimate military target. He's the command and control source. He's not the legitimate leader of Libya and the way to get this to end is to go after the people around him and his support system."
Reminded that assassinating foreign leaders is illegal, Graham said: "In my view, he's not a foreign leader, he's a murderer."
John McCain, another Republican senator who specialises in foreign affairs, told CBS: "We should be taking out his command and control. If he is killed or injured because of that, that's fine."
Michele Bachmann, a Republican congresswoman considering seeking the Republican presidential nomination who was also on the Sunday talk shows, said it was foolish of Barack Obama to have become involved in Libya. She told Fox: "When President Obama went in, his doctrine was to enter Libya for humanitarian purposes. The point of what I am saying is that we are seeing many, many lives lost, including innocent civilians' lives.