The Conservative Party, likely to be dominant after the general election on September 9th, still officially supports applying for membership.
However, they are supported in this by less than a third of their own party members, and just 19.2 percent of the wider population, according to the pollsters.
Norwegians narrowly voted against joining the European Union in a referendum held in 1972, when 46.5 percent voted in favour and 53.5 percent against.
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A second referendum, held in 1994, was closer still with 47.8 percent voting in favour, and 52.2 percent against.