  We discuss the symmetry properties of the reparametrization invariant model
of an interacting relativistic particle where the electromagnetic field is
taken as the constant background field. The direct coupling between the
relativistic particle and the electromagnetic {\it gauge} field is a special
case of the above with a specific set of subtleties involved in it. For the
above model, we demonstrate the existence of a time-space noncommutativity (NC)
in the spacetime structure from the symmetry considerations alone. We further
show that the NC and commutativity properties of this model are different
aspects of a unique continuous {\it gauge} symmetry that is derived from the
non-standard gauge-type symmetry transformations by requiring their consistency
with (i) the equations of motion, and (ii) the expressions for the canonical
momenta, derived from the Lagrangians. We provide a detailed discussion on the
noncommutative deformation of the Poincar{\'e} algebra.
