The letter also contained a clear call to the Prime Minister, in the presidency of the European Union, to put closer integration on the agenda for the weekend EU summit in Cardiff, which Mr Blair will be chairing.
But as Mr Blair completed a hectic round of jet diplomacy in the capitals of Europe, Downing Street last night hailed the letter as a diplomatic coup for the Prime Minister's call for a "third way" between federalism and Euro-scepticism.
The two leaders said: "It cannot be the goal of European policy to establish a European central state, that is to say, a centrally structured Europe. We must do all we can ... to preserve and foster the diversity and richness of Europe's political, cultural and regional traditions and characteristics."
The Prime Minister's spokesman said their letter echoed Mr Blair's speech to the French National Assembly on 3 March calling for a third way in Europe, integrating where it made sense but emphasising the need for subsidiarity, allowing countries to decide their own laws where appropriate.
The Government is keen to see closer cooperation on diplomacy and defence over issues such as Kosovo.
The joint letter urged Mr Blair at the Cardiff summit to order home affairs and justice ministers to draw up a plan of action for the December meeting in Vienna.
That closely fits in with Britain's approach to closer cooperation across borders on tackling crime.
Downing Street said Britain supported closer integration on pollution, the environment, tackling crime and drugs smuggling.
The letter was being seen at Downing Street as a "highly significant" step away from a European super-state, which the Euro-sceptics had insisted was on the agenda.
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