Kosovo's declaration of independence is "unique" and does not set a precedent for other separatist movements in Europe, David Miliband has said.
Mr Miliband said the EU had provided leadership over Kosovo
The UK foreign secretary said the situation could not be equated to that of the Basques in Spain and France.
Mr Miliband said European nations had given "clear leadership" to Serbs and Kosovars, adding there was a "future for co-operation" over the issue.
Kosovo's parliament declared independence from Serbia on Sunday.
The move has divided EU members, with the UK, Germany, Italy and France supporting it and Spain and Romania among opponents.
Serbian security forces were driven out of Kosovo in 1999 after a Nato bombing campaign aimed at halting the violent repression of ethnic Albanian separatists.
The province has been under UN administration and Nato protection since then.
Mr Miliband told BBC Radio 4's Today programme: "What makes it unique is that for nine years there's been a UN protectorate within the independent country of Serbia.
"That does mean that this is a unique case, and I think it's not one that can be equated to the Basque issue or some of the other issues that have been raised."
The EU has adopted a compromise proposal from Spain, which says Kosovo's independence is a breach of international law and will boost separatists everywhere.
To ease those concerns, an EU statement says that Kosovo does not set a precedent and leaves it up to each member state to decide on their future relations.
Mr Miliband said: "I understand the fears, but I think we've seen the dangers of the European Union standing aside, and we did so in the 1990s to catastrophic effect.
"What you've seen here is clear political leadership from the European Union as a whole, and from its constituent members, to be clear to all sides - Serbs as well as Kosovars - about the future for co-operation, if they're willing to take it."
Serbia has recalled its ambassador to Washington in protest at the US's recognition of an independent Kosovo and has threatened to withdraw other envoys.
Belgrade is counting on Russia to veto Kosovo joining the UN as a new nation.