The Libyan regime's claims that Nato is attempting to assassinate Muammar Gaddafi have intensified following the apparent death of one of the leader's sons and three of his grandchildren in an air strike on Tripoli.

Gaddafi was at the one-storey house in a residential area of Tripoli when the missile struck late on Saturday, according to the government spokesman Moussa Ibrahim.

In a rare acknowledgement that security around Gaddafi may not be watertight, Ibrahim told reporters that intelligence about Gaddafi's whereabouts or plans must have been leaked to Nato.

The missile struck the house of Saif al-Arab, 29, the youngest and least well-known of Gaddafi's seven sons, just after 8pm on Saturday during a family gathering. The three grandchildren who were killed were under the age of 12, said Ibrahim.

David Cameron insisted that Nato was acting within the remit of the UN security council resolution, which authorised military actions to protect civilians.

But officials in Russia and Venezuela criticised the attack. "More and more facts indicate that the purpose of the anti-Libyan coalition is to physically destroy Gaddafi," said Konstantin Kosachev, a Russian legislator.

Nato said it had carried out a precision strike against a known command and control building. "All Nato's targets are military in nature and have been clearly linked to the Gaddafi regime's systematic attacks on the Libyan population and populated areas. We do not target individuals," said Lieutenant General Charles Bouchard, commander of Nato's Operation Unified Protector.

"I am aware of unconfirmed media reports that some of Gaddafi's family members may have been killed," he said. "We regret all loss of life, especially the innocent civilians being harmed as a result of the ongoing conflict. Nato is fulfilling its UN mandate to stop and prevent attacks against civilians with precision and care – unlike Gaddafi's forces, which are causing so much suffering."

The strike came hours after Gaddafi called for a ceasefire in the two-and-a-half-month civil war in a speech delivered live on Libyan state television. The Libyan government has repeatedly said it is ready for a political resolution to the conflict and a ceasefire, while continuing to launch military assaults on opposition forces, particularly in Misrata and the western mountains region.

"We renew our call for peace and negotiations," said Ibrahim following the air strike. "What we have now is the law of the jungle. How is this helping in the protection of civilians?"

Cameron declined to comment on the "unconfirmed report", but told the BBC: "The targeting policy of Nato and the alliance is absolutely clear. It is in line with UN resolution 1973 and it is about preventing a loss of civilian life by targeting Gaddafi's war-making machine. That is obviously tanks and guns and rocket launchers, but also command and control as well."

The Libyan regime will use the apparent death of close members of Gaddafi's family to reinforce its claims that Nato is acting illegitimately and that Libya is a victim of a western plot to topple Gaddafi.

UN resolution 1973 permits military action to protect Libyan civilians, which has been interpreted as covering Libyan military facilities, such as command and control centres, as well as military equipment in the field. It does not permit the specific targeting of individuals.

However some politicians in the west have urged Nato to target Gaddafi. "We must cut the head of the snake off," US senator Lindsey Graham said a week ago after the bombing of a building within Gaddafi's Tripoli compound.

Journalists taken to the scene of Saif al-Arab's house in a smart neighbourhood of the capital reported seeing an unexploded missile lying amid shattered concrete and twisted metal. A large crater exposed what appeared to be an underground bunker.

In his 80-minute speech on Libyan state TV in the early hours of Saturday morning, Gaddafi said: "I'm not leaving my country. No one can force me to leave my country, and no one can tell me not to fight for my country."

He described Nato's military intervention in Libya as "a massacre".