Campaigners want the Scottish Government to hold three separate ballots in each of the island groups on Thursday 25 September - one week after the Scottish independence referendum.
If the vote is against independence, the follow-up ballot would be to determine if each island is to become an independent country or to remain within Scotland.
In the event of a yes vote in the referendum on Scottish independence, the islanders would be asked if they wish to stay in the UK
The Scottish Parliament published the petition submitted by Malcom Lamont yesterday.
The petition statement said: "The three island groups are culturally very different but they share a history of having been part of Norway.
"In each island group, there are people who have expressed support for local independence, and there are also people who have said that, in the event that Scotland becomes independent, they would want their island group to leave Scotland and remain in the UK."
Lewis-based Catriona Murray, secretary of the group Referenda On The Islands said: "We have received messages of support from people with islands connections living in Glasgow, Edinburgh, Wales, England, and from one 80-year old Shetland lady in New Zealand."
"We believe that it is up to islanders to decide, and that now is the time to do so. Our own group includes supporters of all three options."
The petition is available at www.scottish.parliament.uk/GettingInvolved/Petitions/islandgroups