The source said: “This is all very unhelpful and very unnecessary. Running this thing and then selling it is hard enough, and a row between the Government and its principal military adviser is about the last thing anybody needs right now.”
The row threatened to overshadow the Prime Minister’s declaration that the military mission against Libya had, so far, been a success.
The mission is poised to enter a new phase in the coming days as Americans hand control of the operation to European nations.
Last night, there were reports that coalition missile strikes had once again hit the dictator’s residence in Tripoli. A loud explosion was followed by a heavy burst of anti-aircraft fire. Missiles also struck Sebha, a stronghold of Gaddafi’s Guededfa tribe, and a naval base six miles east of Tripoli.
A Libyan government spokesman claimed that strikes had hit Sirte airport and several ports, causing casualties.
Earlier, Mr Cameron said that Western forces had prevented a “bloody massacre” in the coastal city of Benghazi and it was now up to the Libyan people to determine their own future.
Speaking in the House of Commons, the Prime Minister acknowledged that there was uncertainty over the next step in Libya. The Americans have admitted that a stalemate could emerge in the North African country, which is effectively split in half.
Mr Cameron said: “Tough action is needed now to ensure that people in Libya can lead their lives without fear and with access to the basic needs of life.
“But we already know, beyond any doubt, that we have succeeded in chasing Gaddafi’s planes out of the sky, we have saved the lives of many Libyans, and we have helped to prevent the destruction of a great and historic city.”
The number of air strikes against the regime dropped sharply after American commanders indicated that Col Gaddafi’s air defences had been largely destroyed. The dictator’s forces were reported to have withdrawn from the rebel-held stronghold of Benghazi.
Although a limited number of air strikes will continue, the focus of the operation will switch to patrolling Libyan airspace and monitoring any movement of regime forces. Later in the week, the military is expected to assist in humanitarian missions to help those in rebel-held areas.
A senior defence source said: “The first phase of the operation has been successful. The mission is now primarily going to be a mix of patrolling and a lot of reconnaissance work. There will be a humanitarian phase.” However, there were growing doubts about the “endgame”, with some predicting a stalemate that could see British forces involved for months.
Mr Cameron and President Barack Obama said yesterday that Col Gaddafi needed to be removed from power.
But American officials said their mission was not to target Col Gaddafi and they had little information as to his whereabouts.
In Britain, ministers were dragged into an increasingly acrimonious dispute over whether the dictator could legally be a target.
The Whitehall spat unfolded after a British missile strike on the Libyan dictator’s compound in Tripoli in the early hours of Monday.
Britain, the US, France and their allies are attacking Libyan targets under a UN edict authorising the use of military force to prevent Gaddafi attacking civilians.
William Hague, the Foreign Secretary, signalled that Gaddafi could be targeted if he ordered attacks on civilians. “The things that are allowed depend on how people behave. It depends on the circumstances,” Mr Hague told BBC Radio Four.
But hours after Mr Hague spoke, the Chief of the Defence Staff was asked if Britain was targeting the Libyan leader personally.
Sir David replied: “Absolutely not. It is not allowed under the UN resolution and it is not something I want to discuss any further.”