You might be interested in controlled version of $-I$. Despite the fact that you can neglect global phase in case of non-controlled gates, you cannot do so in case of controlled version.
The controled gate $-I$ is described by matrix
\begin{pmatrix}
1 & 0 & 0 & 0\\
0 & 1 & 0 & 0\\
0 & 0 & -1 & 0\\
0 & 0 & 0 & -1\\
\end{pmatrix}.
This gate set a phase to $\pi$ (note that $\mathrm{e}^{i\pi} = -1$) if control qubit is in state $|1\rangle$.
To implement the gate simply put $Z$ gate on first qubit (i.e. control qubit) and nothing (i.e. identity operator) on second qubit (i.e. target qubit). You can check that the matrix above is really equal to $Z \otimes I$ and hence the proposed construction really implements the requested gate.