Ri-congruence is defined for partial n-ary groupoids as a generalization of right congruence of a full binary groupoid. It is proved that for any i the Ri-congruences of a partial n-ary groupoid G form a lattice, where the congruence lattice of G is not necessary a sublattice. An example is given, demonstrating that the congruence lattice of a partial n-ary groupoid is not always a sublattice of the equivalence relations lattice of G. The partial n-ary groupoids G are characterized such that for some i, all the equivalence relations on G are its Ri-congruences.