The Defence Secretary Liam Fox says he agrees with the head of the Armed Forces that Nato needs to intensify its campaign in Libya.
General Sir David Richards told the Sunday Telegraph direct attacks should be launched against the infrastructure propping up Colonel Gaddafi's regime.
He said it was necessary to prevent the Libyan dictator remaining in power.
But the UN's under-secretary general for humanitarian relief called for a temporary cessation of hostilities.
Baroness Amos, the UN's under-secretary for humanitarian relief, said there was an urgent need for an end to the conflict and she was concerned that "any upscaling" in the fighting would have a significant impact on innocent civilians.
Speaking to Radio 4's The World This Weekend, she said: "Of course there is a military imperative. Of course there is a political aspect to it. But there are others who are working on those aspects. My job is to make sure that we all remember that it is the innocent people who are suffering and that we need a political solution as quickly as we can."
The UK and other countries have been bombing Libya under a UN resolution authorising force to protect civilians.
The Security Council resolution authorises "all necessary measures" to protect civilians under threat of attack - short of an occupying force.
The views of Gen Richards, Chief of the Defence Staff, are said to be supported by other senior Nato officers.
They argue increasing the range of targets from direct threats such as tanks and command sites would be legitimate, but would require the backing of member states.'Within rules'
Col Gaddafi's removal is not a specified military objective of the action.
But in the interview with the Telegraph, Gen Richards said it would be "within the rules" should he be killed in a strike on a command and control centre.
He said the "vice is closing on Gaddafi but we need to increase the pressure further through more intense military action".
He said: "The military campaign to date has been a significant success for Nato and our Arab allies. But we need to do more.
"If we do not up the ante now there is a risk that the conflict could result in Gaddafi clinging to power.
"At present, Nato is not attacking infrastructure targets in Libya. But if we want to increase the pressure on Gaddafi's regime then we need to give serious consideration to increasing the range of targets we can hit."
Gen Richards added there had been "hardly any civilian casualties as a result of the extreme care Nato has taken in the selection of bombing targets".