"I believe this is the first time a constitution is being drafted basically on the Internet," Thorvaldur Gylfason, a member of the constitutional council, told Britain's Guardian newspaper. "The public sees the constitution come into being before their eyes."
The current constitution dates from independence from Denmark in 1944 and is just the Danish constitution with a few words changed.
The council is posting draft clauses on its Web site, and the public comments there or on a Facebook page. The panel's meetings are open to the public and streamed live online.
The draft document is to be complete by the end of July and then put to a referendum.
"There's been a lot of good will for what we are trying to do. The public has added much to our debate," Gylfason said.
The constitution provides for separation of powers to prevent a repeat of the financial crisis and changes elections to the Parliament, the Althing, which dates from 930.