  For $k \geq 1$, in a graph $G=(V,E)$, a set of vertices $D$ is a distance
$k$-dominating set of $G$, if any vertex in $V\setminus D$ is at distance at
most $k$ from some vertex in $D$. The minimum cardinality of a distance
$k$-dominating set of $G$ is the distance $k$-domination number, denoted by
$\gamma_k(G)$. An ordered set of vertices $W=\{w_1,w_2,\ldots,w_r\}$ is a
resolving set of $G$, if for any two distinct vertices $x$ and $y$ in
$V\setminus W$, there exists $1\leq i\leq r$, such that $d_G(x,w_i)\neq
d_G(y,w_i)$. The minimum cardinality of a resolving set of $G$ is the metric
dimension of the graph $G$, denoted by $dim(G)$. In this paper, we introduce
the distance $k$-resolving dominating set, which is a subset of $V$ that is
both a distance $k$-dominating set and a resolving set of $G$. The minimum
cardinality of a distance $k$-resolving dominating set of $G$ is called the
distance $k$-resolving domination number and is denoted by $\gamma^r_k(G)$. We
give several bounds for $\gamma^r_k(G)$ some in terms of the metric dimension
$dim(G)$ and the distance $k$-domination number $\gamma_k(G)$. We determine
$\gamma^r_k(G)$ when $G$ is a path or a cycle. Afterwards, we characterize the
connected graphs of order $n$ having $\gamma^r_k(G)$ equal to $1$, $n-2$, and
$n-1$, for $k\geq 2$. Then, we construct graphs realizing all the possible
triples $(dim(G),\gamma_k(G),\gamma^r_k (G))$, for all $k\geq 2$. Later, we
determine the maximum order of a graph $G$ having distance $k$-resolving
domination number $\gamma^r_k(G)=\gamma^r_k\geq 1$, we provide graphs achieving
this maximum order for any positive integers $k$ and $\gamma^r_k$. Finally, we
establish Nordhaus-Gaddum bounds for $\gamma^r_k(G)$, for $k\geq 2$.
