The UN has not given coalition forces the "legal authority" to remove Libyan leader Muammar Gaddafi by military action, David Cameron has said.
The UK prime minister told Parliament a UN resolution allowing strikes on the country was "limited in its scope".
The head of the armed forces said it "absolutely" did not allow the targeting of Colonel Gaddafi.
But there is some confusion, as Defence Secretary Liam Fox has said such action is "potentially a possibility".
Coalition forces, including those from the UK, France and the US, say they are trying to protect civilians from attacks by the ruling regime.
BBC political editor Nick Robinson said the UK government was walking a "legal tightrope" with the UN resolution and wanted to reassure Arab countries that it was not about "to topple" Col Gaddafi - and that Libya would not become "another Iraq".
On the other hand, the coalition did not want to risk "telling Gaddafi what they will do", our correspondent added.
United Nations Resolution 1973, passed last week, authorises "all necessary measures" short of an occupying force to protect citizens - but there have been questions about exactly what that could mean.
During a second night of missile strikes in Libya, Col Gaddafi's sprawling Bab al-Aziziya complex was hit. Western journalists taken to the compound were shown a ruined building.
On Sunday Dr Fox, asked whether Col Gaddafi himself was a legitimate target, said it could "potentially be a possibility, but you mention immediately one of the problems we would have, which is that you would have to take into account any civilian casualties that might result from that".
And Foreign Secretary William Hague did not rule out the possibility in an interview on Monday, adding he would not "speculate on the targets".
But, amid reports Col Gaddafi could himself be targeted, General Sir David Richards, Chief of the Defence Staff, told the BBC: "No, absolutely not. It's not allowed under the UN resolution and it's not something I want to discuss any further."
MPs are debating the UK's involvement in military action in the country, culminating in a vote at about 2200 GMT in the Commons.
Mr Cameron said Libyan air defences had been "neutralised" and that the world could not "stand aside while this dictator murders his own people".
The prime minister added: "But the UN resolution is limited in its scope. It explicitly does not provide legal authority for action to bring about Gaddafi's removal from power by military means.
"As I've said, we will help fulfil the UN Security Council [resolution] - it is for the Libyan people to determine their government and their destiny.
"But our view is clear - there is no decent future for Libya with Colonel Gaddafi remaining in power."
However, government sources told the BBC, in response to Gen Richards' comments, that, under the UN resolution, there was the power to target him if he was a threat to the civilian population of Libya.
US Defence Secretary Robert Gates said expanding the goal of protecting civilians could divide what he described as a "very diverse coalition".