"In addition to the individual nations which have a sovereign position ... the Arctic Council is becoming a key decision-making forum," Clinton told EUobserver Thursday.
The council, made up of eight countries with territory in the polar region, was established in 1996 in Ottawa. Clinton and officials of the other nations were in Nuuk for a conference.
The council includes Canada, Denmark, Finland, Iceland, Norway, Russia, Sweden and the United States.
Six organizations representing Arctic indigenous peoples have status as "permanent participants."
Discussions in Greenland were to cover climate change, melting icecaps, offshore oil and new shipping routes.
At the meeting, Sweden assumed a two-year chairmanship of the council, replacing Denmark.
"In the past this was an area of political conflict, now it's becoming an area of increasing cooperation," Swedish Foreign Minister Carl Bildt said in reference to international negotiations on arctic issues.