David Cameron, Barack Obama and Nicolas Sarkozy have signalled their determination to fight on in Libya until Muammar Gaddafi is gone.
In a joint article, the British, American and French leaders warned it would be an "unconscionable betrayal" were Nato to cut and run with the dictator still in power.
Gaddafi must "go and go for good" before rebuilding of the country could begin, they said - dismissing calls for an immediate ceasefire.
The defiant statement came as warplanes were again heard over Tripoli, accompanied by air raid sirens and loud explosions.
However, as the military operation approaches the end of its first month there is little sign of a breakthrough on the ground, where rebels appear more than matched by the government's forces.
Nato secretary general Anders Fogh Rasmussen has also had to appeal for more planes to conduct air strikes, with many member states unwilling to join the front line.
Although the US have officially stepped back from an active combat role, President Obama's involvement in the latest statement may quell speculation about the strength of his commitment.
In their piece - published in The Times, The Washington Post and Le Figaro - the leaders insisted: "It is unthinkable that someone who has tried to massacre his own people can play a part in their future government.
"The brave citizens of those towns that have held out against forces that have been mercilessly targeting them would face a fearful vengeance if the world accepted such an arrangement. It would be an unconscionable betrayal."
The leaders added: "So long as Gaddafi is in power, Nato and its coalition partners must maintain their operations so that civilians remain protected and the pressure on the regime builds... Britain, France and the United States will not rest until the UN Security Council resolutions have been implemented and the Libyan people can choose their own future."
