Prime Minister David Cameron has warned that difficult days still lie ahead for opposition fighters in Libya, as he admitted the Nato command was unsure of Muammar Gaddafi's whereabouts.

Speaking outside Number 10 on Monday morning, Cameron said there was "no room for complacency" over the situation but insisted that Libya was on the road to "freedom and democracy."

The prime minister was keen to emphasise the differences in approach between the current government's intervention in Libya and the previous government's ventures in Iraq and Afghanistan, saying: "We have tried to learn lessons of the past." He pointed out that in Libya, Britain had acted within the framework of a UN Security Council and had not committed ground troops to the country.

While acknowledging that Muammar Gaddafi's regime is "falling apart and is in full retreat", Cameron admitted that Nato forces currently didn't know Gaddafi's location. He reiterated calls for the Libyan leader to go, but insisted it was for the new government of Libya, formed from the country's National Transitional Council (NTC), to decide how the Libyan dictator should be tried for crimes against humanity. He said Gaddafi must "give up any claim he has to control Libya".

"The situation in Tripoli is clearly very fluid," he said, adding the British government would support the will of the Libyan people. Britain is already assisting the Libyans by sending medical supplies to "near where they are needed." Cameron told reporters that the UK would establish a diplomatic presence in Tripoli "as soon as it is safe to do so".

"This should be a Libya-led and owned process ... coordinated by UN." He said a British diplomatic mission would be set up in Tripoli "as soon as possible".

"We are working closely with the NTC to support their plans to make sure that happens."

Cameron said the wider Nato mission in Libya would "continue for as long as needed" and that Britain would ensure medical and humanitarian supplies were deployed to the World Health Organisation near Tripoli.

He added frozen foreign assets would be released but did not give a specific time frame. Speaking more broadly about the demonstrations and revolutions across the region so far this year, the prime minister described the Arab Spring as: "A great opportunity for north Africa and the Middle East."

But speaking immediately afterwards on Sky News defence secretary Liam Fox took a more triumphalist tone, saying David Cameron's view that the action in Libya was legal and right had been "vindicated". Fox also suggested Germany may want to "re-evaluate" their decision not to play a full role in the action.

Earlier US President Barack Obama said the country was "slipping from the grasp of a tyrant" and urged Gaddafi to step aside and prevent further bloodshed.

"The future of Libya is now in the hands of the Libyan people," he said in a statement on Sunday.