RIPOLI (AFP) – The leaders of Britain, France and the United States said a Libyan future including Moamer Kadhafi is "unthinkable", as the defiant fist-pumping strongman toured the streets of Tripoli.

Western powers struggled meanwhile to stay united over a NATO-led air campaign that has so far failed to budge Kadhafi from power.

In a bid to put on a united front, however, British Prime Minister David Cameron, France's President Nicolas Sarkozy and US President Barack Obama penned a joint article dismissing a Libyan future with Kadhafi as "unthinkable" and an "unconscionable betrayal" by the rest of the world.

"It is unthinkable that someone who has tried to massacre his own people can play a part in their future government," said the article, which appeared Friday in the London Times, The Washington Post and French daily Le Figaro.

Responding, Kadhafi's daughter Aisha said calls for her father to step down were an insult to all Libyans.

"To speak of Kadhafi's resignation is a humiliation for all Libyans," she said in a brief statement at her father's Tripoli residence before hundreds of young supporters late Thursday.

Her father had earlier in the day toured the streets of the capital in an open-top 4x4, sporting shades and a hunting hat and hailing bystanders with clenched fists.

"God, Libya, Moamer and no one else," supporters chanted as loud explosions rocked the Bab al-Aziziya neighbourhood home to Kadhafi's residence and a base for most foreign journalists in the capital.

NATO initially denied it had again bombed Tripoli, but an alliance spokesman later acknowledged that raids had targeted the outskirts.

"Late mission reports from pilots returning from Libya indicate there appear to be two additional strikes that were conducted at targets closer to the city of Tripoli," a NATO official told AFP on condition of anonymity.

Cracks opened up in NATO as Washington rebuffed French appeals for more assistance with the enforcement of the UN Security Council resolution authorising all necessary means to protect Libyan civilians.

French Foreign Minister Alain Juppe made a personal appeal to US Secretary of State Hillary Clinton for Washington to resume major air raids in Libya, but he said his plea was rebuffed.

"I told her we needed them back, we would have liked them to return," Juppe said, adding that Clinton said US planes would continue to fly on a case-by-case basis.

With nearly 100,000 US troops fighting a grinding war in Afghanistan, Washington pulled back around 50 combat planes from Libyan operations last week after handing over control of the mission to NATO, but they have since participated in some missions to take out Kadhafi's air defences.

A senior US official said the United States was performing a quarter of all missions and that it saw no need to do more on the military front.

"We have said all along that we want to see allies step up and that we are certainly doing at least our fair share," the official said.

The port area of Libya's besieged third city Misrata came under heavy attack by Kadhafi's forces, who fired dozens of Grad missiles and tank shells that killed at least 13 people and wounded 50, a rebel spokesman said.

The key crossroads town of Ajdabiya on the front line between the rebel-held east and the mainly government-held west, recaptured from loyalist forces over the weekend, also came under renewed assault on Thursday.

But the town was calm on Friday, an AFP reporter said, with around 30 rebel cars grouped at its western edge.

At an international conference hosted by the Arab League in Cairo, UN chief Ban Ki-moon called for a "political" solution and immediate ceasefire, while European Union foreign policy chief Catherine Ashton urged Kadhafi to resign immediately.

A NATO declaration said the allies "strongly endorse" calls for Kadhafi to leave power.

Alliance foreign ministers played down any rift after France and Britain pressed allies to contribute more combat jets to the mission and intensify the raids against regime tanks and artillery shelling civilians.

"We are also sharing the same goal which is to see the end of the Kadhafi regime in Libya. And we are contributing in many ways in order to see that goal realised," said Clinton.

"The US is committed to our shared mission. We will strongly support the coalition until our work is completed."

German Foreign Minister Guido Westerwelle, whose country shocked allies by refusing to back the UN resolution authorising the military operation, said NATO supports the aspirations of the Libyan people.

"We are united by the common goal, that we want a free and democratic Libya. The dictator Kadhafi, who started a civil war against his own people, must go," Westerwelle said at a two-day meeting of NATO foreign ministers in Berlin.

But differences remained over the air raids against forces threatening the population, which are being conducted by just six of the 28 allies. Rebels have urged NATO to step up the air campaign as the mission has failed to shift the balance of power so far.

NATO Secretary General Anders Fogh Rasmussen said a Wednesday meeting in Qatar of the international contact group on Libya, which promised the rebels cash and the means to defend themselves, "laid out a good foundation."

"We will now discuss how we can continue the military operation leading to a successful result," he said.

Military action was first launched by Britain, France and the United States on March 19, but NATO took over the operation two weeks ago after overcoming French reservations about letting the Western military organisation alliance lead it.