The letter from the three leader was published in the UK's Times newspaper as well as the
International Herald Tribune and France's Le Figaro.
The BBC's Paul Adams, reporting from Washington, says the letter is an unusual step at a time of unease over Nato's ongoing mission.
Only a few of Nato's 28 members - including France, the UK, Canada, Belgium, Norway and Denmark - are conducting air strikes.
The alliance's Secretary General Anders Fogh Rasmussen told foreign ministers at a meeting in Berlin he had received no offers from any ally to supply the extra jets, but said he remained hopeful.
Signed by US President Barack Obama, British Prime Minister David Cameron and French President Nicolas Sarkozy, the letter says Libyans in cities like Misrata and Ajdabiya continue to suffer "terrible horrors at Gaddafi's hands".
While the coalition has no mandate to remove Col Gaddafi by force, "it is impossible to imagine a future for Libya with Gaddafi in power", the leaders say.
To allow him to remain in power "would be an unconscionable betrayal" of Libya's people, they argue, and would make Libya both "a pariah state [and] a failed state".
Nato pilots are enforcing a UN resolution to establish a no-fly zone and to protect civilians in Libya. The country has effectively been split between forces for and against Col Gaddafi since a revolt against his rule began in mid-February.
"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," the letter continues.
"Then a genuine transition from dictatorship to an inclusive constitutional process can really begin, led by a new generation of leaders."
The letter holds out the prospect of reconstruction for Libya with the help of the "UN and its members".
But French Defence Minister Gerard Longuet, speaking on French radio, conceded that ousting Col Gaddafi would be "certainly" beyond the scope of the existing UN resolution, and could require a new Security Council vote.
New fightingFighting on the ground, as well as Nato bombing missions, has continued while politicians debate the way forward.
Rebels said a rocket attack in Misrata by pro-Gaddafi forces killed 23 people on Thursday, and there were new reports of rocket fire into the city on Friday morning. Neither account could be confirmed.
The BBC's Orla Guerin entered the besieged western Libyan city, visiting a hospital where staff were battling to treat civilians injured by mortars and rocket fire.
The intensive care unit was full of patients with multiple shrapnel injuries, including a six year old girl, our correspondent says. Doctors say 80% of those killed or injured in the city are civilians.
The hospital is struggling to keep pace with the attacks, and its emergency ward is a tent in the car park, she reports. Patients are rushed in and out to make way for new arrivals.
Medical supplies are coming ashore here but there has been heavy shelling in the port area, raising fears that Col Gaddafi wants to cut this last link to the outside world, she adds.
In Berlin, Anders Fogh Rasmussen said Nato would continue "day by day, strike by strike" to target Col Gaddafi's forces.
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Samad Majeed Fazal
