Traditional recommender systems estimate user preference on items purely based on historical interaction records, thus failing to capture fine-grained yet dynamic user interests and letting users receive recommendation only passively. Recent conversational recommender systems (CRSs) tackle those limitations by enabling recommender systems to interact with the user to obtain her/his current preference through a sequence of clarifying questions. Recently, there has been a rise of using knowledge graphs (KGs) for CRSs, where the core motivation is to incorporate the abundant side information carried by a KG into both the recommendation and conversation processes. However, existing KG-based CRSs are subject to two defects: (1) there is a semantic gap between the learned representations of utterances and KG entities, hindering the retrieval of relevant KG information; (2) the reasoning over KG is mostly performed with the implicitly learned user interests, overlooking the explicit signals from the entities actually mentioned in the conversation. To address these drawbacks, we propose a new CRS framework, namely, the Knowledge Enhanced Conversational Reasoning (KECR) model. As a user can reflect her/his preferences via both attribute- and item-level expressions, KECR jointly embeds the structured knowledge from two levels in the KG. A mutual information maximization constraint is further proposed for semantic alignment between the embedding spaces of utterances and KG entities. Meanwhile, KECR utilizes the connectivity within the KG to conduct explicit reasoning of the user demand, making the model less dependent on the user’s feedback to clarifying questions. As such, the semantic alignment and explicit KG reasoning can jointly facilitate accurate recommendation and quality dialogue generation. By comparing with strong baselines on two real-world datasets, we demonstrate that KECR obtains state-of-the-art recommendation effectiveness, as well as competitive dialogue generation performance.