The Libyan regime is preparing to make a fresh overture to the international community, offering concessions designed to end the bloodshed of the three-month-long civil war.

The Independent has obtained a copy of a letter from the country's Prime Minister, Al-Baghdadi al-Mahmoudi, being sent to a number of foreign governments. It proposes an immediate ceasefire to be monitored by the United Nations and the African Union, unconditional talks with the opposition, amnesty for both sides in the conflict, and the drafting of a new constitution.

David Cameron and Barack Obama met yesterday to try to find an exit strategy from a conflict increasingly appearing to have no definitive military solution in sight. The US President acknowledged that the allies now seem to face a long, attritional campaign.

Behind the scenes, there are signs that Western powers may agree to a ceasefire without the precondition of Muammar Gaddafi and his immediate family going into exile.

Both the British Prime Minister and the US President declared yesterday that the Libyan dictator must leave the country. However senior officials from both sides of the Atlantic increasingly indicate that talks should start if the regime forces end their military action, and there are also genuine signs that Colonel Gaddafi is relinquishing direct control of the state apparatus.

Unusually, Dr Mahmoudi's letter makes no mention of Colonel Gaddafi's role in the country's future. Previous regime communiqués have insisted that the Colonel will fight on, while other proposals, notably by his son Saif al-Islam, envisaged Colonel Gaddafi staying on as a figurehead as a period of transition gets under way.

The alliance led by Britain, France and the US has put its stock in backing the Libyan revolutionaries. Although the rebels in the port of Misrata have thrown back regime troops besieging their city, the main rebel force in the east of the country has failed to make any headway despite two months of Nato bombing. Meanwhile the opposition's political leadership, based in Benghazi – some of them senior former regime officials – insists that no talks can be held until Colonel Gaddafi and his family go into exile.

Whitehall sources say there is a widespread feeling that the Cameron government "set the bar too high" in stating that the departure of the Libyan leader was a prerequisite for a deal to end the strife.

"They thought he would do a runner like Ben Ali [in Tunisia] and Mubarak [in Egypt]," said one. "We know we will have to deal with members of the regime in the future. After all, a lot of the rebel council are former regime people. We should give the people in Tripoli some wriggle room to help them ease out Gaddafi."

Dr Mahmoudi's letter stated: "The future Libya will be radically different to the one that existed three months ago. That was always the plan. Only now we may need to accelerate the process. But to do so, we must stop the fighting, start talking, agree on a new constitution and create a system of government that both reflects the reality of our society and conforms to the demands of contemporary governance.

"We must immediately make humanitarian assistance available to all Libyans in need whether they are in Libya or outside. The cycle of violence must be replaced by a cycle of reconciliation. Both sides need the incentive to move out of their corner and to engage in a process that will lead to consensus."

The Libyan Prime Minister's initiative follows meetings held with Ban Ki-moon which led to the United Nations Secretary General calling for an "immediate, verifiable ceasefire". The UN's special envoy in Libya, Abdel Elah al-Khatib, had discussed specific conditions needed for this with Dr Mahmoudi and a select few regime officials.

The official government estimate of the cost of Libyan military operations for the UK alone is £100m so far, although independent defence analysts claim it adds up to three times that figure. However there is no doubt that this is likely to escalate significantly with the ratcheting up of operations which this week saw the heaviest bombing of Tripoli so far.

Britain and France are sending attack helicopters to take part in Libyan operations, and the RAF is said to be considering sending more Tornado GR4 jets. The firepower from the aircraft is considered to be necessary as the range of targets within Libya is widened.

Advocates of military action hold that it is the intensification of attacks which is driving the regime to seek a deal. According to defence officials, more than 1,200 targets have been "degraded" since the start of operations.

Extract from the letter