Attempts to manage the globalisation of the world economy should not lead to regulation which would slow down the circulation of capital, both President Clinton and the British Prime Minister, Mr Blair, warned their centre-left colleagues at the seminar in Florence.
A week before the Seattle World Trade Organisation (WTO) ministerial meeting to start a new trade round, both leaders insisted that the new left must embrace free trade and free capital movements as they had already financial rigour domestically.
Mr Blair insisted they must take care that their efforts to manage the world economy did not become a form of protectionism.
Mr Clinton said that although the volume of currency transactions was 15 times greater than the volume of trade - at 1 trillion transactions a day - this was necessary to the functioning of the market. But he acknowledged that attempts by Chile and Malaysia to slow down speculative money flows in and out of their economies were credible because of the patent integrity of both governments. The same could not be said of Russia.
But this cautious approach on the part of Mr Clinton and Mr Blair to the regulation of the international trade system did not agree altogether with the approach of some of their colleagues.
The German Chancellor, Mr Gerhard Schroder, warned of the need for "greater transparency to check what is happening in the financial markets" and of doing something about "private speculators who can wipe out entire economies".
And President Henrique Cardoso of Brazil spoke of a "deficit of governance at the global level". Of the WTO round, he warned: "If what is to prevail is the undiluted logic of power, the result will be nothing more than the export of unemployment by the stronger countries."
Responding to the British and US leaders' appeals to support free movement of capital, and by implication to support a multilateral agreement on investment, one of the most controversial North-South points of difference in the coming WTO round, Mr Cardoso accepted that his country needed capital.
But, he said, it had to be on the basis of a new transparency and accountability of the international financial institutions. Why, he asked, could G8 not be expanded to include nations of millions of people whose fate depended on its decisions?
The differences were nuanced, however - Mr Blair also spoke of the need for transparency and reform of the financial institutions - but all the leaders' comments were premised on what the Italian Prime Minister, Mr Massimo D'Alema, characterised as the rejection of conservative passivism in the face of globalisation. "Not all solutions are in the market. There is room for politics too," he insisted.
Mr Clinton said their analysis had to start from an understanding of the revolutionary character of the technological transformation of society and the unparalleled explosion of world trade which had laid the basis in the US for the unprecedented peacetime growth now being manifested.
It was happening "because we underestimated the productivity gains of new technology and the powers of open frontiers to restrain inflation," he said.
But there were people being passed by by such changes and the growing skills gap could intensify inequality, Mr Clinton warned. So the challenge for the centre-left was to emphasise the role of the state in empowering individuals through lifelong education. The US, Mr Clinton said, had been involved in issuing some million micro-credit loans at the village level in Brazil. He believed the world community should set itself the target of 200 million such loans in the developing world.
Mr Blair said that it was wrong to contrapose economic and social priorities. "We live in a new era when human capital will determine success," he said. The state's central role was thus to help people prosper in that new environment.
Speaking on Saturday night, the new President of the European Commission, Mr Romano Prodi, laid claim to his centre-left credentials with a strong defence of the European Social Model.
Mr Prodi described the welfare state as the "greatest single achievement of Western democracies and one of the greatest of the 20th Century.
"According to conventional wisdom you would expect countries with good social safety nets to perform badly in economic terms. But in fact quite opposite is true. The welfare state, by ensuring that more people take part in economic life, actually stimulates economic growth. Social protection far from being a burden, must be regarded as a productive factor."