Some 67% of 1,000 Swedes questioned said they wanted to vote on the treaty in a referendum, while 29% said parliament should decide. The survey was commissioned by the June List, a eurosceptic party not represented in parliament, which published the results on its website.
A large majority of those questioned, 64 %, said a 2003 Swedish referendum vote to keep the Swedish krona and reject the euro was ”a good decision”, while twenty-nine percent said the result was a bad decision.
The opposition Green and Left parties called last month for a referendum to be held on the EU treaty, which is aimed at streamlining EU decision-making.
A previous draft of the the treaty, officially called the European Constitution, was rejected by public votes in both France and the Netherlands.
Sweden is one of seven EU countries to have delayed ratification of the constitution, which cannot come into force unless it is ratified by all 27 member states.
Prime Minister Fredrik Reinfeldt has indicated that he plans to ask parliament to vote on the text.