  We evaluate the impact of an external magnetic field on the chiral symmetry
and confinement-deconfinement transition temperatures by using a vector-vector
contact interaction model for quarks regularized so as to include an explicit
confining scale in the corresponding gap equation. Exploring the evolution of
the chiral condensate and the confining scale with temperature $T$ and magnetic
field strength $eB$ ($e$ represents the fundamental electric charge), we
determine the pseudo-critical temperatures for the chiral ($T_c^\chi$) and
deconfinement ($T_c^c$) transitions from their inflection points, respectively.
By construction, $T_c^\chi= T_c^c$ in the chiral limit. Within a mean field
approximation, we observe the magnetic catalysis phenomenon, characterized by a
rising behavior of $T_c^\chi$ and $T_c^c$ with growing $eB$. Considering a
lattice inspired running coupling which monotonically decreases with $eB$,
inverse magnetic catalysis takes place in our model. We explore the role of the
magnetic field in the traits of the confinement-deconfinement transition
described by the model. Our findings are also in agreement with predictions
derived from effective models of strong interactions.
