Natural graphite minerals with global reserves greater than 320 million tones can be considered as low-cost and highly available precursors for the preparation of high-quality carbon nanostructures with potential applications in energy devices and related areas. Here, the electrochemical conversion of natural graphite minerals into carbon nanostructures, comprising onion-like carbon nanoparticles and multiwall carbon nanotubes (MWCNTs) in high-temperature molten salts are studied. The galvanostatic polarization of electrodes made of such minerals is conducted in molten LiCl and LiCl-NaCl at various current densities, leading to the exfoliation of the minerals into carbon nanostructures. The influence of non-carbon impurities present in the natural graphite mineral, and the current density applied on the characteristics of the resultant nanocarbons are investigated. Moreover, the structural and microstructural properties of the nanocarbons fabricated using natural graphite minerals are compared with those produced using commercially pure graphite electrodes. It is found that the electrochemical nanostructuring of the mineral in molten salt not only increases the surface area of the material, but also increases its electrical conductivity. The high-yield conversion of the mineral into carbon nanostructures is realized at the cathode current density of around 1 A cm^-2. The Li- and Na- ion storage performances of this sample are evaluated. The Li-ion storage capacity of the sample is found to be remarkable at around 460 mAh g^-1 after 500 charge/discharge cycles at the current density of 200 mA g^-1. The green molten salt preparation and the electrochemical performance of nanocarbons is discussed here.