Read David Cameron's full statement on events in Libya in full on politics.co.uk.
I have just come from chairing a meeting of the National Security Council on the situation in Libya.
The latest information is that the vast majority of Tripoli is now controlled by free Libyan fighters, although fighting continues – and some of it is extremely fierce.
We have no confirmation of Qadhafi’s whereabouts, but at least two of Qadhafi’s sons have been detained.
His regime is falling apart and in full retreat.
Qadhafi must stop fighting, without conditions – and clearly show that he has given up any claim to control Libya.
As for his future, that should be a decision for Chairman Jalil and the new Libyan authorities.
The situation in Tripoli is clearly very fluid today and there can be no complacency.
Our task now is to do all we can to support the will of the Libyan people, which is for an effective transition to a free, democratic and inclusive Libya.
This will be a Libyan-led and Libyan-owned process with broad international support co-ordinated by the UN – and I am in close contact with partners from NATO, the Arab League and with Chairman Jalil himself.
Clearly the immediate priority today is to establish security in Tripoli.
We are working closely with the NTC to support their plans to make sure that happens.
I spoke to Chairman Jalil last week, and will be speaking to him again, to agree with him the importance of respecting human rights, avoiding reprisals, and making sure all parts of Libya can share in the country’s future.
And the wider NATO mission which is to protect civilians – that will continue for as long as it is needed.
This morning the National Security Council also discussed the urgent work that needs to be done on medical supplies and humanitarian aid, on diplomatic efforts, and on our work at the UN Security Council.
Let me say a word about each.
First, on the need to support the medical facilities in Tripoli.
We have already deployed medical supplies close to where they are needed, and have now released them to the World Health Organisation.
In the coming days it will be important to make sure the communications networks, the electricity, the power supplies, fuel and water are maintained or repaired where they need to be.
The National Transitional Council have been planning for this for months and we have been helping with that work.
Diplomatically, we have a strong mission already in Benghazi consisting of Foreign Office, military and aid specialists, and we will establish a British diplomatic presence in Tripoli as soon as it is safe and practical to do so.
This will include stabilisation experts who have been planning for this moment with the NTC for months.
At the UN, we will also be taking early action in the Security Council to give the new Libyan authorities the legal, diplomatic, political and financial support they need.
We will soon be able to release the frozen assets that belong to the Libyan people.
The Foreign Secretary is returning and, with the Deputy Prime Minister, the Defence Secretary and the Development Secretary, will coordinate our efforts with the NTC in the week ahead.
Six months ago this country took the difficult decision to commit our military to support the people of Libya.
I said at the time that this action was necessary, legal and right – and I still believe that today.
It was necessary because Gadhafi was going to slaughter his own people – and that massacre of thousand of innocent people was averted.
Legal, because we secured a Resolution from the United Nations, and have always acted according to that Resolution.
And right, because the Libyan people deserve to shape their own future, just as the people of Egypt and Tunisia are now doing.
I would like to take this opportunity to thank the many British pilots, air staff, ground crew and everyone who worked so hard to support the NATO mission and the work of the NTC.
On the pilots – as ever they have sho0wn incredible bravery, professionalism and dedication.
This has not been our revolution, but we can be proud that we have played our part.
There will undoubtedly be difficult days ahead.
No transition is ever smooth or easy.
But today the Arab spring is a step further away from oppression and dictatorship and a step closer to freedom and democracy.
And the Libyan people are closer to their dream of a better future.