Let $k$ be a number field. Recall that Faltings proved the famous Tate conjecture, which states that for any abelian variety $X$ over $k$ and any prime $\ell$, the natural map $$\mathrm{End}(X) \otimes \mathbb{Q}_\ell \to \mathrm{End}(V_\ell(X))^{\mathrm{Gal}(\bar k/k)},\qquad (*)$$ is an isomorphism, where $V_\ell(X)$ denotes the usual Tate module of $X$ tensored with $\mathbb{Q}_\ell$.

If I understand it correctly however, this is but one part of the Tate conjecture, which in general states that the cycle class map $$A^r(X) \otimes \mathbb{Q}_\ell \to H^{2r}(\bar X, \mathbb{Q}_\ell)^{\mathrm{Gal}(\bar k/k)},$$ is an isomorphism for all $r$. The "Tate conjecture" as I state it in $(*)$ is but the case $r=1$ of this conjecture.

Is the full Tate conjecture still open for abelian varieties? Are there any interesting special cases where it is known?