Offline handwriting recognition systems require cropped text line images for both training and recognition. On the one hand, the annotation of position and transcript at line level is costly to obtain. On the other hand, automatic line segmentation algorithms are prone to errors, compromising the subsequent recognition. In this paper, we propose a modification of the popular and efficient multi-dimensional long short-term memory recurrent neural networks (MDLSTM-RNNs) to enable end-to-end processing of handwritten paragraphs. More particularly, we replace the collapse layer transforming the two-dimensional representation into a sequence of predictions by a recurrent version which can recognize one line at a time. In the proposed model, a neural network performs a kind of implicit line segmentation by computing attention weights on the image representation. The experiments on paragraphs of Rimes and IAM database yield results that are competitive with those of networks trained at line level, and constitute a significant step towards end-to-end transcription of full documents.