Supporters of a plan to let local authorities decide on citizenship procedures appear to have the upper hand six weeks ahead of a nationwide vote in June.
An opinion poll - commissioned by the Swiss Broadcasting Corporation and published on Friday - says supporters have a margin of 11 per cent over opponents, but fall just short of the necessary majority.
About 15 per cent of respondents were still undecided.
The poll is based on just over 1,200 interviews carried out across Switzerland in mid-April.
The rightwing Swiss People's Party proposal seeks to overturn a ban on ballot box decisions over citizenship applications imposed in the wake of a series of controversial results.
The Federal Court outlawed such a procedure in 2003, saying applications, which can be handled by special panels or town hall meetings, must be subject to appeal.
The government and three out of four major political parties have come out against the People's Party proposal, saying it paves the way for discriminatory and arbitrary decisions.
On June 1 voters will also decide on a proposal to limit information campaigns by the federal authorities ahead of nationwide ballots and a plan to reform the health insurance system.
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