Opening the last UN general assembly of this century, Mr Annan spoke of the discrepancies between the organisation's failure to act in the face of the 1994 Rwandan genocide, Nato's attack on Yugoslavia over Kosovo without even a mandate from the Security Council, and most recently the dispatch of an international, UN-backed force to East Timor - but only with the prior approval of Indonesia.
If the new commitment to intervene was to retain the support of public opinion around the world, he said, "it must be, and be seen to be, fairly and consistently applied, irrespective of region or nation. Humanity after all is indivisible."
With his speech, Mr Annan immediately set the tone of an assembly certain to be dominated by the issue of where - and how - to draw the line between national sovereignty, and the right of the international community to step in to end a manifest injustice. But agreement will be anything but easy.
President Abdelaziz Bouteflika of Algeria - which has consistently opposed any outside "interference" to help to resolve its own bloody internal turmoil - rejected any UN intervention without the express prior approval of the government of the country involved.
The secretary general said it had been "a tragedy" that the Security Council, which was required by the UN's founding charter to defend the "common interest" had not presented a united front over Kosovo. Globalisation was making the UN more important than ever, he argued, but similar failures in future could destroy its credibility.
Mr Annan joined the French Prime Minister, Lionel Jospin, in making clear that the UN could do nothing without money. In a pointed reference to the US, which is up to $1.5bn in arrears on its contributions to the world body, Mr Jospin urged "all countries" to meet their financial obligations. If Washington does not come up with at least $250m by the end of the year, it risks being stripped of its voting rights in the general assembly.
Britain is earmarking a special contingent of police officers for UN peace-keeping operations. The move, announced by the Foreign Secretary, Robin Cook, to the general assembly last night, involves up to 200 men, 40 to 50 of whom will constitute a rapid response squad available for immediate deployment. It follows Britain's decision to put the equivalent of a brigade of troops on permanent stand-by for UN operations.