Nowadays, great quantities of data are produced by a large and diverse family of sensors (e.g., remote sensors, biochemical sensors, wearable devices), which typically measure multiple variables over time, resulting in data streams that can be profitably organized as multivariate time-series. In practical scenarios, the speed at which such information is collected often makes the data labeling task uneasy and too expensive, so that limit the use of supervised approaches. For this reason, unsupervised and exploratory methods represent a fundamental tool to deal with the analysis of multivariate time series. In this paper we propose a deep-learning based framework for clustering multivariate time series data with varying lengths. Our framework, namely DeTSEC (Deep Time Series Embedding Clustering), includes two stages: firstly a recurrent autoencoder exploits attention and gating mechanisms to produce a preliminary embedding representation; then, a clustering refinement stage is introduced to stretch the embedding manifold towards the corresponding clusters. Experimental assessment on six real-world benchmarks coming from different domains has highlighted the effectiveness of our proposal.