  In this paper we present an accurate numerical scheme for extracting
inter-atomic exchange parameters ($J_{ij}$) of strongly correlated systems,
based on first-principles full-potential electronic structure theory. The
electronic structure is modelled with the help of a full-potential linear
muffin-tin orbital method. The effects of strong electron correlations are
considered within the charge self-consistent density functional theory plus
dynamical mean-field theory (DFT+DMFT). The exchange parameters are then
extracted using the magnetic force theorem, hence all the calculations are
performed within a single computational framework. The method allows to
investigate how the $J_{ij}$-parameters are affected by dynamical electron
correlations. In addition to describing the formalism and details of the
implementation, we also present magnetic properties of a few commonly discussed
systems, characterised by different degrees of electron localisation. In bcc Fe
we found a minor renormalisation of the $J_{ij}$ interactions once the
dynamical correlations are introduced. However, generally, if the magnetic
coupling has several competing contributions from different orbitals, the
redistribution of the spectral weight and changes in the exchange splitting of
these states can lead to a dramatic modification of the total interaction
parameter. In NiO we found that both static and dynamical mean-field results
provide an adequate description of the exchange interactions, which is somewhat
surprising given the fact that these two methods result in quite different
electronic structures. By employing Hubbard-I approximation for the treatment
of the $4f$ states in hcp Gd we reproduce the experimentally observed multiplet
structure. The calculated exchange parameters result to be rather close to the
ones obtained by treating the $4f$ electrons as non-interacting core states.
