Foreign Secretary David Miliband has suggested the European Union should work towards including Russia, Middle Eastern and North African countries.
He said enlargement was "our most powerful tool" for extending stability.
In his first major speech on the UK's relationship with Europe, he said the EU would not become a "superpower" but should be a "role model" for the world.
It could be a "model power of regional co-operation" dedicated to free trade, the environment and tackling extremism.
He said the EU must "keep our promises to Turkey", adding: "If we fail.... it will signal a deep and dangerous divide between east and west.
"Beyond that we must keep the door open, retaining the incentive for change and the prospect of membership provides."
Mr Miliband made his address at the College of Europe in Bruges, Belgium, where Baroness Thatcher delivered her famous warning against "some sort of identikit European personality" almost exactly two decades ago in September 1988.
US 'only superpower'
Mr Miliband said that speech had been "haunted by demons - a European superstate bringing in socialism by the back door".
But he said: "The truth is that the EU has enlarged, remodelled and opened up. It is not and is not going to become a superstate. But neither is it destined to become a superpower."
He said the goal "must be a multilateral free-trade zone around our periphery".
This would be a "version of the European Free Trade Association that could gradually bring the countries of the Mahgreb, the Middle East and Eastern Europe in line with the single market, not as an alternative to membership, but potentially as a step towards it".
People have NOT mentioned this AT ALL....You need to check out: ecfr.eu! There is a power struggle here, EU vs. US. Go look.
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