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The government wants to reserve powers to regulate the domain name industry and so guarantee that the public interest will underpin the operation of the UK domain name space.
Critics believe that government control will lead to more red tape and slower resolutions of disputes over issues such as cyber-squatting.
Nominet has called on members to vote through changes in its constitution that it says would achieve the government's goals but keep its self-regulatory role and independence.
Isoc president and CEO Lynn St Amour said, "The internet works best when everyone that uses it is able to have their views heard about how it should grow and develop, and to participate in its development."
She said was encouraged by Nominet's proposal to include a public purpose commitment in its constitution. "The Internet Society would particularly like to support the proposal to open up Nominet's decision-making processes to many more stakeholders."
Isoc and Nominet had a long history of collaboration, said St Amour. "We are happy to support Nominet's efforts as they work to ensure that the voice of the ordinary internet user can be heard now and into the future," she said.
Nominet CEO Lesley Cowley said the domain registrar had to prove that it was balanced, catered for the needs of all stakeholders, and was governed according to best practice standards.
"It is in our members' interests that we make the constitutional changes to support this and we urge them to vote in favour for the changes necessary to retain internet self-regulation," she said.
Nominet will hold an extraordinary general meeting on 24 February in London to vote on the proposals.