Pressure for the West to intervene increased after the killing of two orphans in an evacuation attempt, but John Major rejected demands for more action by Lord Owen, the former SDP leader.
'We are not dealing with an orthodox war, a single enemy, a front line, or clearly identifiable targets. Nor do I detect any support in Parliament or in public opinion for operations which would tie down large numbers of British forces in difficult and dangerous terrain for a long period,' Mr Major told Lord Owen in a letter.
The pressure will be intensified today by Paddy Ashdown, the Liberal Democrat leader, who will renew his calls for air strikes against heavy weapons pounding Sarajevo when he returns to London from a visit to Bosnia and Croatia.
It is likely the pressure will grow as the death toll mounts, but Mr Major made it clear that he was pinning his hopes on the London conference on 26 August, which Britain had arranged as the holder of the EC presidency, for achieving a UN-EC peace initiative.
He said that this was 'not the time to think of a military solution - we could not unite the international community behind such a policy'.
The Prime Minister confirmed that the armed forces had carried out a contingency study for armed intervention, but ruled out air strikes and ground attacks as being too difficult.
Mr Major was replying to a letter by Lord Owen last week making an impassioned appeal for action to force a ceasefire. 'What we cannot sensibly undertake is an operation which would begin with an ultimatum but might lead to a commitment to some form of international protectorate in Bosnia-Hercegovina, sustained indefinitely by military force,' Mr Major said.
But Mr Major said there may be 'other ways in which armed forces may become useful'. Downing Street said he had not ruled out using air power to protect air corridors.
Lord Owen said: 'It may be that the UN will be sucked into Yugoslavia for some years, but the UN was sucked into Cyprus for a long a time.' He rejected as 'nonsense' the warning by Boutros Boutros-Ghali, the UN Secretary- General, that it would become a Vietnam.