Distance learning has been expanding. Learner engagement is particularly important in project-based learning (PBL), but the interaction between teacher and learner and the understanding of learner status, including engagement, is not easy. This study aims to support teacher-learner communication based on learner engagement for remote PBL. In this paper, we propose the use of video activity reports by learners to estimate and understand learner engagement and to demonstrate its feasibility on the basis of the relationship between verbal and nonverbal information that can be obtained from video activity reports and learner engagement. Analysis of 232 video activity reports submitted by eight graduate students while working on remote research-based PBLs reveals that learner engagement decreases (1) when the report contained negative words, (2) when filled pauses were frequent or long, and (3) when silent pauses were infrequent or short. Furthermore, the feasibility of an AI-based support system is demonstrated through the design and implementation of a prototype.