The simulation of human behaviors in virtual environments has many applications. In many of these applications, situations arise in which the user has a face-to-face interaction with a virtual agent. In this work, we present an approach for multi-agent navigation that facilitates a face-to-face interaction between a real user and a virtual agent that is part of a virtual crowd. In order to predict whether the real user is approaching a virtual agent to have a face-to-face interaction or not, we describe a model of approach behavior for virtual agents. We present a novel interaction velocity prediction (IVP) algorithm that is combined with human body motion synthesis constraints and facial actions to improve the behavioral realism of virtual agents. We combine these techniques with full-body virtual crowd simulation and evaluate their benefits by conducting a user study using Oculus HMD in an immersive environment. Results of this user study indicate that the virtual agents using our interaction algorithms appear more responsive and are able to elicit more reaction from the users. Our techniques thus enable face-to-face interactions between a real user and a virtual agent and improve the sense of presence observed by the user.