The task of Human-Object Interaction (HOI) detection targets fine-grained visual parsing of humans interacting with their environment, enabling a broad range of applications. Prior work has demonstrated the benefits of effective architecture design and integration of relevant cues for more accurate HOI detection. However, the design of an appropriate pre-training strategy for this task remains underexplored by existing approaches. To address this gap, we propose $\textit{Relational Language-Image Pre-training}$ (RLIP), a strategy for contrastive pre-training that leverages both entity and relation descriptions. To make effective use of such pre-training, we make three technical contributions: (1) a new $\textbf{Par}$allel entity detection and $\textbf{Se}$quential relation inference (ParSe) architecture that enables the use of both entity and relation descriptions during holistically optimized pre-training; (2) a synthetic data generation framework, Label Sequence Extension, that expands the scale of language data available within each minibatch; (3) ambiguity-suppression mechanisms, Relation Quality Labels and Relation Pseudo-Labels, to mitigate the influence of ambiguous/noisy samples in the pre-training data. Through extensive experiments, we demonstrate the benefits of these contributions, collectively termed RLIP-ParSe, for improved zero-shot, few-shot and fine-tuning HOI detection performance as well as increased robustness to learning from noisy annotations. Code will be available at https://github.com/JacobYuan7/RLIP.