Multi-document summarization (MDS) refers to the task of summarizing the text in multiple documents into a concise summary. The generated summary can save the time of reading many documents by providing the important content in the form of a few sentences. Abstractive MDS aims to generate a coherent and fluent summary for multiple documents using natural language generation techniques. In this paper, we consider the unsupervised abstractive MDS setting where there are only documents with no groundtruh summaries provided, and we propose Absformer, a new Transformer-based method for unsupervised abstractive summary generation. Our method consists of a first step where we pretrain a Transformer-based encoder using the masked language modeling (MLM) objective as the pretraining task in order to cluster the documents into semantically similar groups; and a second step where we train a Transformer-based decoder to generate abstractive summaries for the clusters of documents. To our knowledge, we are the first to successfully incorporate a Transformer-based model to solve the unsupervised abstractive MDS task. We evaluate our approach using three real-world datasets from different domains, and we demonstrate both substantial improvements in terms of evaluation metrics over state-of-the-art abstractive-based methods, and generalization to datasets from different domains.