The council includes all European nations except Belarus
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Leaders from 46 European countries are meeting at a two-day summit of the Council of Europe in Poland.
The Warsaw summit is seeking a new mandate to promote democracy, human rights and rule of law across Europe.
Polish President Aleksander Kwasniewski told the summit that Western nations had a duty to support democratic reforms in eastern Europe.
The human rights watchdog was Europe's first international organisation to be set up after World War II.
The BBC's Adam Easton, in Warsaw, says the Strasbourg-based council is undergoing something of an identity crisis.
He says its role as Europe's main human rights watchdog is now under threat from the enlarged European Union - which increased its members from 15 to 25 last year.