We study cylindrically symmetric Abelian wormholes in ($4+n$)-dimensional Kaluza-Klein theory. It is shown that static, four-dimensional, cylindrically symmetric solutions in ($4+n$)-dimensional Kaluza-Klein theory with maximal Abelian isometry group $\mathrm{U}(1{)}^n$ of the internal space with diagonal internal metric can be obtained, as in the case of a supersymmetric static black hole [M. Cvetič and D. Youm, Phys. Rev. D 52, 2144 (1995)], only if the isometry group of the internal space is broken down to the $\mathrm{U}(1{)}_e\times \mathrm{U}(1{)}_m$ gauge group; they correspond to dyonic configurations with one electric ($Q_e$) and one magnetic ($Q_m$) charge that are related either to the same $\mathrm{U}(1{)}_e$ or $\mathrm{U}(1{)}_m$ gauge field or to different factors of the $\mathrm{U}(1{)}_e\times \mathrm{U}(1{)}_m$ gauge group of the effective six-dimensional Kaluza-Klein theory. We find new exact solutions of the six-dimensional Kaluza-Klein theory with two Abelian gauge fields, a dilaton field and a scalar field, associated with the internal metric. We obtain new types of cylindrically symmetric wormholes supported by the radial and longitudinal electric and magnetic fields.

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