Implicit Discourse Relation Recognition (IDRR) involves identifying the sense label of an implicit connective between adjacent text spans. This has traditionally been approached as a classification task. However, some downstream tasks require more than just a sense label and the specific connective used. This paper presents Implicit Sense-labeled Connective Recognition (ISCR), which identifies the implicit connectives as well as their sense labels between adjacent text spans. ISCR can be treated as a classification task, but it's actually difficult due to the large number of potential categories, the use of sense labels, and the uneven distribution of instances among them. Accordingly, this paper instead handles ISCR as a text-generation task, using an encoder-decoder model to generate both connectives and their sense labels. Here, we explore a classification method and three types of text-generation methods. From our evaluation results on PDTB-3.0, we found that our classification method outperforms the conventional classification-based method.