The following are excerpts from that speech, which was broadcast live.
We cannot begin today without reflecting on yesterday's anniversary - on the criminal challenge so brutally thrown in our faces on 11 September 2001.
The terrorist attacks of that day were not an isolated event.
They were an extreme example of a global scourge which requires a broad, sustained and global response. Broad, because terrorism can be defeated only if all nations unite against it.
Every government that is committed to the rule of law at home must be committed also to the rule of law abroad. All states have a clear interest, as well as a clear responsibility, to uphold international law and maintain international order.
On almost no item on our agenda does anyone seriously contend that each nation, or any nation, can fend for itself. Even the most powerful countries know that they need to work with others, in multilateral institutions, to achieve their aims.
Individual states may defend themselves, by striking back at terrorist groups and the countries that harbour or support them. But only concerted vigilance and co-operation among all states, with constant, systematic exchange of information, offers any real hope of denying terrorists their opportunities.
On all these matters, for any one state - large or small - choosing to follow or reject the multilateral path must not be a simple matter of political convenience.
'Legitimacy essential'
When states decide to use force to deal with broader threats to international peace and security, there is no substitute for the unique legitimacy provided by the United Nations.
The leadership of Iraq continues to defy mandatory resolutions adopted by the Security Council under Chapter VII of the Charter.
I have engaged Iraq in an in-depth discussion on a range of issues, including the need for arms inspectors to return, in accordance with the relevant Security Council resolutions.
Efforts to obtain Iraq's compliance with the Council's resolutions must continue.
I urge Iraq to comply with its obligations - for the sake of its own people, and for the sake of world order. If Iraq's defiance continues, the Security Council must face its responsibilities.
Let us all recognise, from now on - in each of our capitals, in every nation, large and small - that the global interest is our national interest.