In the paper is introduced for a given algebra $\mathcal A$, the notion of a weak partial congruence algebra $K_w(\mathcal A)=(C_w(A),\wedge,\vee,0,^-1,\Delta,\sigma,A^2\cdot C_w(A)$ is the set of weak congruences of the algebra $\mathcal A$ i.e. of all the symmetric and transitive subalgebras of $\mathcal A\times\mathcal A$ (see [3]). It is shown that $K_w(\mathcal A)$ gives more information on $\mathcal A$ than just lattice $C_w(\mathcal A)$. Also considered is the corresponding abstract weak partial congruence algebra and proved that a theorem of representation does not hold for it.