We present the first supercluster catalogue constructed with the extended ROSAT-ESO Flux-Limited X-ray (REFLEX II) Galaxy Cluster survey data, which comprises 919 X-ray selected galaxy clusters with a flux limit of 1.8x10^-12^erg/s/cm2. Based on this cluster catalogue we construct a supercluster catalogue using a friends-of-friends algorithm with a linking length depending on the (local) cluster density, which thus varies with redshift. The resulting catalogue comprises 164 superclusters at redshift z<=0.4. The choice of the linking length in the friends-of-friends method modifies the properties of the superclusters. We study the properties of different catalogues such as the distributions of the redshift, extent and multiplicity by varying the choice of parameters. In addition to the supercluster catalogue for the entire REFLEX II sample, we compile a large volume-limited cluster sample from REFLEX II with the redshift and luminosity constraints of z<=0.1 and L_X_>=5x10^43^erg/s. With this catalogue we construct a volume-limited sample of superclusters. This sample is built with a homogeneous linking length, and hence selects effectively the same type of superclusters. By increasing the luminosity cut we can build a hierarchical tree structure of the volume-limited samples, where systems at the top of the tree are only formed via the most luminous clusters. This allows us to test if the same superclusters are found when only the most luminous clusters are visible, comparable to the situation at higher redshift in the REFLEX II sample. We find that the selection of superclusters is very robust, independent of the luminosity cut, and the contamination of spurious superclusters among cluster pairs is expected to be small. Numerical simulations and observations of the substructure of clusters suggest that regions of high cluster number density provide an astrophysically different environment for galaxy clusters, where the mass function and X-ray luminosity function are shifted to higher cut-off values and an increased merger rate may also boost some of the cluster X-ray luminosities. We therefore compare the X-ray luminosity function for the clusters in superclusters with that for the field clusters with the flux- and volume-limited catalogues. The results mildly support the theoretical suggestion of a top-heavy X-ray luminosity function of galaxy clusters in regions of high cluster density.