  This is a sequel to the paper [F. Breuer, H.-G. R\"uck, Drinfeld modular
polynomials in higher rank, J. Number Theory 129 (2009), 59-83.], in which we
introduced Drinfeld modular polynomials of higher rank, using an analytic
construction. These polynomials relate the isomorphism invariants of Drinfeld
F_q[T]-modules of rank r\geq 2 linked by isogenies of a specified type. In the
current paper, we give an algebraic construction of greater generality, and
prove a generalization of the Kronecker congruences relations, which describe
what happens when modular polynomials associated to P-isogenies are reduced
modulo a prime P. We also correct an error in [loc. cit.].
